In the small hours of 25 February 1983, the playwright Tennessee Williams died in his suite at the Elysée, a small, pleasant hotel on the outskirts of the Theatre District in New York City. He was 71: unhappy, a little underweight, addicted to drugs and alcohol and paranoid sometimes to the point of delirium. According to the coroner's report, he'd choked on the bell-shaped plastic cap of a bottle of eyedrops, which he was in the habit of placing on or under his tongue while he administered to his vision.

The next day, the New York Times ran an obituary claiming him as "the most important American playwright after Eugene O'Neill", though it had been two decades since his last successful play. It listed his three Pulitzer prizes, for A Streetcar Named Desire, Cat on a Hot Tin Roof and Night of the Iguana, adding: "He wrote with deep sympathy and expansive humour about outcasts in our society. Though his images were often violent, he was a poet of the human heart."

He was also a kind, generous, hard-working man, who rose at dawn almost every morning of his life, sitting down at his typewriter with a cup of black coffee to produce what would amount to well over 100 short stories and plays. At the same time, he was a lonely, depressed alcoholic who managed by degrees to isolate himself from almost everyone he loved. A sample entry from his diary in 1957 reads: "Two Scotches at bar. 3 drinks in morning. A daiquiri at Dirty Dick's, 3 glasses of red wine at lunch and 3 of wine at dinner. Also two seconals so far, and a green tranquillizer whose name I do not know and a yellow one I think is called reserpine or something like that" – an itemisation made more troubling by the fact that he was in rehab at the time.

Things got worse in 1963, when Williams's long-term partner Frank Merlo, nicknamed the Little Horse, died of lung cancer. After that, he was far gone and out, barely perpendicular against the current, buoyed on a diet of coffee, liquor, barbiturates and speed. Hardly any wonder he found speech difficult, or kept toppling over in bars, theatres and hotels. Each year he put on a new play, and each year it failed, rarely lasting a month before it closed.

Two years before he died, Williams was interviewed in the Paris Review. He talked about his work and the people he had known, and he touched too, a little disingenuously, on the role of alcohol in his life, saying: "O'Neill had a terrible problem with alcohol. Most writers do. American writers nearly all have problems with alcohol because there's a great deal of tension involved in writing, you know that. And it's all right up to a certain age, and then you begin to need a little nervous support that you get from drinking."

While not all of this statement is wholly to be believed, it's true that Williams was by no means the only alcoholic writer in America, or anywhere else for that matter. Ernest Hemingway. F Scott Fitzgerald. William Faulkner. John Cheever. Patricia Highsmith. Truman Capote. Dylan Thomas. Jack London. Marguerite Duras. Elizabeth Bishop. Jean Rhys. Hart Crane. These are among the greatest writers of our age, and yet, like Williams, their addiction to alcohol damaged their creativity, ravaged their relationships and drove many of them to death.

Why do writers drink? Discussing Edgar Allan Poe, Baudelaire once commented that alcohol had become a weapon "to kill something inside himself, a worm that would not die". In his introduction to Recovery, the posthumously published novel of the poet John Berryman, Saul Bellow observed: "Inspiration contained a death threat. He would, as he wrote the things he had waited and prayed for, fall apart. Drink was a stabiliser. It somewhat reduced the fatal intensity." In Cat on a Hot Tin Roof, Williams explains the desire even more succinctly. Towards the end of the play, Brick, the former football hero, tells his father that he needs to keep drinking until he hears "the click…This click that I get in my head that makes me peaceful. I got to drink till I get it." Horrified, Big Daddy grabs his son's shoulders, exclaiming: "Why boy, you're alcoholic."

I was 17 when I first read that sentence, and already well acquainted with alcoholism. My mother's partner for a decade, Diana, had been a drinker, and our time together had recently ended in disaster, when the police came to our home and arrested her after a violent altercation. It wasn't just the fights that had frightened me, but rather the terrifying sense that someone was no longer inhabiting consensual reality. I was traumatised, I suppose, and it's hard to express the relief I experienced when I opened up my pale green copy of Cat and found within its pages a brave, brazen account of the role alcohol can play within a family; a house. Ever since that afternoon, I've been preoccupied by what writers have to say about drinking, especially those who have been drinkers themselves.

Over time, I grew most interested in six American writers whose lives intersected in odd, sometimes uncanny ways. All but one had – or saw themselves as having – that most Freudian of pairings, an overbearing mother and a weak father. All were tormented by self-hatred and a sense of inadequacy. Three were profoundly promiscuous, and almost all experienced conflict and dissatisfaction with regard to their sexuality. Most died in middle age, and the deaths that weren't suicides tended to be directly related to the years of hard and hectic living. At times, all tried in varying degrees to give up alcohol but only two succeeded, late in life, in becoming permanently dry.

These sound like tragic lives, the lives of wastrels or dissolutes, and yet these six men – Tennessee Williams, Ernest Hemingway, F Scott Fitzgerald, John Cheever, John Berryman and Raymond Carver – produced between them some of the most beautiful writing this world has ever seen. As the novelist Jay McInerney once commented of Cheever: "There have been thousands of sexually conflicted alcoholics but only one of them wrote The Housebreaker of Shady Hill and The Sorrows of Gin." I wanted to know how their writing and drinking had intertwined, and so in 2011 I took a trip across America. Over the course of a month I travelled by plane and train across the country, drifting from New York to New Orleans, Key West, St Paul and Port Angeles. I chose these places because they seemed to serve as staging posts, in which the successive phases of alcohol addiction had been acted out. By travelling through them in sequence, I thought it might be possible to build a kind of topographical map of alcoholism, tracing its developing contours from the pleasures of intoxication through to the gruelling realities of the drying-out process.

I went to New York in search of first drinks. Tennessee Williams took his at sea in the summer of 1928: a green crème de menthe, somewhere on the greyish Atlantic between Manhattan and Southampton. He was still called Tom back then, a skinny, shy boy of 17, travelling with his grandfather and a party of parishioners on a grand tour of Europe. Afterwards he was violently sea sick, later confiding in a letter to his mother that though his grandfather was lapping up the cocktails, his own preference was for Coca-Cola and ginger ale. The pleasures of abstinence soon palled. By the time they reached Paris, he'd discovered champagne.

Tom had been a sickly, delicate boy, and as a teenager began to suffer the panic attacks that would dog him until the very last days of his life. At first he used to self-medicate by pacing the streets of St Louis or swimming frantic lengths in a nearby pool. But as he grew older and moved to New York, sex and alcohol became his preferred methods of managing stress. In his autobiography, Memoirs, he remembered how after drinking wine "you felt as if a new kind of blood had been transfused into your arteries, a blood that swept away all anxiety and all tension for a while, and for a while is the stuff that dreams are made of".

He was by no means the only writer who used alcohol in this way. The same trick was employed by John Cheever, one of the greatest short-story writers of his or any century. Cheever fascinated me because he was, in common with many alcoholics, a helpless mixture of fraudulence and honesty. Though he feigned patrician origins, his upbringing in Quincy, Massachusetts was both financially and emotionally insecure, and while he eventually attained all the trappings of the landed Wasp he never managed to shake a painful sense of shame and self-disgust.

He was an almost exact contemporary of Williams, and though they weren't friends, their worlds in New York often overlapped. In fact, Mary Cheever first realised her husband wasn't entirely heterosexual when they attended the first Broadway production of A Streetcar Named Desire. According to Cheever, Blake Bailey's beautiful biography, there was a leitmotif associated with Blanche DuBois's dead homosexual husband and this tune lodged in Mary's head and led to some kind of underwater realisation that her husband's sexuality was not as she'd assumed, though this wasn't a thought she shared with him.

Cheever's problem, as anyone familiar with his journals will know, is that the same gulf between appearance and interior that makes his stories – "The Enormous Radio", "The Day the Pig Fell into the Well", "Goodbye, My Brother" – so beguiling was also at work in his own life. Despite an increasingly command performance as an upstanding member of the bourgeoisie, Cheever couldn't shake the sense of being essentially an impostor among the middle classes. Writers, even the most socially gifted and established, must be outsiders of some sort, if only because their job is that of scrutiniser and witness. All the same, Cheever's sense of double-dealing seems to have run unusually deep.

This burden of fraudulence, of needing to keep some lumbering secret self forever under wraps, was not merely a matter of class anxiety. Cheever lived in the painful knowledge that his erotic desires included men, that these desires were antagonistic and even fatal to the social security he also craved, and that as such "every comely man, every bank clerk and delivery boy was aimed at my life like a loaded pistol". During this period, his sense of failure and self-disgust could reach such agonising heights that he sometimes raised in his journals the possibility of suicide.

Who wouldn't drink in a situation like that, to ease the pressure of maintaining such intricately folded double lives? He'd been hitting it hard since he first arrived in New York, back in 1943. Even in the depths of poverty he managed to find funds for nights that might, head-splittingly, take in a dozen Manhattans or a quart apiece of whiskey. He drank at home and in friends' apartments, in the Brevoort, the Plaza and the Menemsha Bar on 57th Street, where he'd pop in after collecting his daughter from school and let her eat maraschino cherries while he attended to his needs. Though not all these scenes were exactly civilised, alcohol was an essential ingredient of Cheever's ideal of a cultured life, one of those rites whose correct assumption could protect him from the persistent shadows of inferiority and shame.

Instead, it did just the opposite. By the late 1950s, Cheever was using the word alcoholism to describe his behaviour, writing grimly: "In the morning I am deeply depressed, my insides barely function, my kidney is painful, my hands shake, and walking down Madison Avenue I am in fear of death. But evening comes or even noon and some combination of nervous tensions obscures my memories of what whiskey costs me in the way of physical and intellectual wellbeing. I could very easily destroy myself. It is 10 o'clock now and I am thinking of the noontime snort."

In order to understand how an intelligent man could get himself into such a dire situation, it's necessary to understand what a glass of champagne or shot of scotch does to the human body. Alcohol is both an intoxicant and a central nervous depressant, with an immensely complex effect upon the brain. A single drink brings about a surge of euphoria, followed by a diminishment in fear and agitation caused by a reduction in brain activity. Everyone experiences these effects, and they are the reason alcohol is such a pleasurable drug; the reason why, despite my history, I too love to drink.

But if the drinking is habitual, the brain begins to compensate for these calming effects by producing an increase in excitatory neurotransmitters. What this means in practice is that when one stops drinking, even for a day or two, the increased activity manifests itself by way of an eruption of anxiety, more severe than anything that came before. This neuroadaptation is what drives addiction in the susceptible, eventually making the drinker require alcohol in order to function at all.

Not everyone who drinks, of course, becomes an alcoholic. The disease, which exists in all quarters of the world, is caused by an intricate mosaic of factors, among them genetic predisposition, early life experience and social influences. As it gathers momentum, alcohol addiction inevitably affects the drinker, visibly damaging the architecture of their life. Jobs are lost. Relationships spoil. There may be accidents, arrests and injuries, or the drinker may simply become increasingly neglectful of their responsibilities and capacity to provide self-care. Conditions associated with long-term alcoholism include hepatitis, cirrhosis, gastritis, heart disease, hypertension, impotence, infertility, various types of cancer, increased susceptibility to infection, sleep disorders, loss of memory and personality changes caused by damage to the brain. More stress, of course: to be drowned out in turn by drink after drink after drink.

This is where the black stories start. This is where you find the bloated, feuding Hemingway of the later years, his liver so swollen it protruded from his gut like a long leech. This is where you find F Scott Fitzgerald, washed up in Baltimore in the mid-1930s, his wife in an asylum, writing bad stories drunk and crashing his car into town buildings. And this is where you find the poet John Berryman, esteemed professor, breaking his bones and vomiting in strangers' cars.

I hate these stories. They're true and they're also untrue, and profoundly distorting. What I discovered as I travelled was how ambiguous and contradictory the issue of writers and alcohol really is. On the one hand, there's dissolution and degradation, and on the other there's dogged labour, compulsive honesty and the production of enduring art. Reading Tennessee Williams's diaries while he was writing Cat on a Hot Tin Roof reveals a man in crisis, so profoundly addicted to alcohol that he carried a flask of whiskey wherever he went. And yet the play he produced is a miracle of truth-telling. It seems impossible that in the midst of such confusion and self-harm, Williams was able to produce a play like Cat, with its uncompromising portrayal of the drinker's urge to evade reality. And yet he retained in some unobliterated part of himself the necessary clarity to set down on paper a portrait of the self-deceiving nature of the alcoholic.

He was not the only one, by any means. From Berryman's Dream Songs to Fitzgerald's Tender Is the Night and Hemingway's For Whom the Bell Tolls, there exist dozens of works of art in which an alcoholic writer reflects on their own disease; a disease, furthermore, that is hallmarked by distortions in thinking, particularly denial. When I travelled to Key West to visit Hemingway's house, I kept thinking in particular about a line in For Whom the Bell Tolls that compares alcoholism to "a deadly wheel… it is the thing that drunkards and those who are truly mean or cruel ride until they die."

There was something sickening about that image. I imagined what it might be like to ride such a wheel: the confusion, the gathering sense of entrapment. Impossible not to think of what lay ahead for Hemingway: the long depression, ECT at the Mayo Clinic, the loss of his home in Cuba, his manuscripts and letters, his beloved boat Pilar. He said it was as if he'd lost his life, and on 2 July 1961 he shot himself in Idaho, 19 days before his 62nd birthday. John Berryman, too, who after several failed cycles of treatment for alcohol addiction caught the morning bus to the Washington Avenue bridge in St Paul on Friday 7 January 1972. He climbed the railing and let himself go, falling 100 feet on to a pier and rolling partway down the embankment of the Mississippi river, where his body was later identified by a blank cheque in his pocket and the name on his broken glasses.

These stories weigh on me, and yet an alcoholic can stop drinking. I knew it from my own childhood, and I knew it from my reading. My mother's ex-partner got dry at a treatment centre she still describes as a hellhole, and came back into our lives sober. John Cheever also managed it. "I came out of prison 20 pounds lighter and howling with pleasure," he wrote in a letter to a Russian friend on 2 June 1975, a few weeks after his release from the Smithers Alcohol Treatment and Training Centre in New York City, and though no cure had been found for his loneliness or sense of sexual confusion, he never drank again. Even when he was dying of cancer, even when all but one of his doctors said he might as well go back on the bottle, he elected to stay dry. For the last seven years of his life he was stone cold sober: still depressed, still at the mercy of his erections, but also in possession of his wit, and the old, magical capacity for being unsprung by joy.

The writer whose sobriety most interested me, however, was Raymond Carver. I'd come across his poems long ago, and been struck by the praiseful way he wrote about his second life: the one in which alcohol was no longer the dominating force. When I'd first thought of taking a trip to America, I knew immediately I wanted to end in Port Angeles, the town on the Olympic Peninsula that had nourished his sobriety.

It's almost impossible to overestimate the hardship of Carver's early adulthood, in which he struggled to educate himself and get food on the table while stealing every spare minute in which to write. In such straitened circumstances, it's not difficult to understand why alcohol might have begun to seem like an ally, or else a key to a locked door. His father had drunk to escape the monotony of work and to ease the pressures of survival. For Ray, there was also bitterness to choke back; bitterness and self-reproach and a sense of spoiling time. These are the sort of things that can sour in your head if you're still working as a janitor at 27, swabbing corridors in Mercy hospital. And these are the sort of things you might try to soothe in the Fireside Lounge on H Street, knocking back a boilermaker at the end of the night shift, readying up for another day with your own exhausting children.

There's no doubt the odds were stacked against him; but nor is there much doubt that he became, six days out of seven, his own worst enemy. The things Carver did seem so senselessly self-destructive. One Raymond – Good Raymond, I suppose – would get on to a master's programme, or find a decent job, and the other Raymond, the perverse, malevolent one, would somehow conspire to mess it up. He published three volumes of poems during his drinking years, and wrote almost 40 short stories, among them "Will You Please Be Quiet, Please?", "Tell the Women We're Going", "Dummy" and "So Much Water So Close to Home". At the same time he was unreliable, paranoid and violent; by his own description a bankrupt, a cheat, a thief and a liar. As for creativity, as he approached the nadir of his drinking he could barely write at all.

Good Raymond emerged from the wreckage slowly, like a man struggling from a sm ashed car. He spent a long time shuttling through recovery, getting dry and then going straight back out to drink. Early on, during the bad years in California, he had a seizure on the floor just as he was about to leave a treatment centre, smashing his forehead open. The doctor warned him that if he ever drank again he risked becoming a wet-brain, a graphic term for alcoholic brain damage. According to his wife, he spent that evening "sucking brandy from a bottle as if it were Pepsi, his stitches concealed under a bandage, indifferent to the doctor's warning".

In 1976 his first volume of stories, Will You Please Be Quiet, Please?, was published. That same year he checked into Duffy's, a private treatment centre in Napa that was later the setting for "Where I'm Calling From". The programme consisted of frequent AA meetings and controlled withdrawal by way of hummers, progressively weaker shots of rotgut bourbon in water, doled out every three hours for three days. Shortly after his release, he announced that he understood he could never drink hard liquor again, and would in future stick to André champagne.

Unsurprisingly, he was back again weeks later, checking himself in on New Year's Eve. It was his last pass through formal treatment. That spring he left his family and rented a house alone, overlooking the Pacific. For the next few months he went to AA meetings and tried, not always successfully, to maintain his balance on the wagon. The turning point came in May, when he was offered an advance of $5,000 for a novel. He was in the midst of a bender at the time, but four days later took his final drink in the Jambalaya bar. "June 2nd 1977", he remembered in the Paris Review. "If you want the truth, I'm prouder of that, that I've quit drinking, than I am of anything in my life. I'm a recovered alcoholic. I'll always be an alcoholic, but I'm no longer a practising alcoholic."

Slowly, over the next two years, he backed away from his family, whose ongoing troubles he felt certain were capable of scuttling his recovery. For a while he barely wrote, and then the new stories started coming; stories infused with "little human connections"; stories he'd "come back from the grave" to write. In the summer of 1978, he fell in love with the poet Tess Gallagher, the protector and companion of his second life. At the time, she'd just built a house in her home town of Port Angeles, and at the tail end of 1982 Ray moved in. It was in this period that he produced – though he might have preferred caught – clutch after clutch of poems, slippery and pristine as the dream salmon he sometimes encountered on his nights in town.

I'd read one of them so many times I'd almost worn a track in it. It's called "Where Water Comes Together With Other Water". "I love creeks and the music they make," the narrator begins, and then lists, exultantly, all the other waterways he knows, and the enlarging effects they have on his heart. He describes how barren his life was 10 years back, and ends with a characteristically heartfelt, sawn-off sentence, a kind of credo or manifesto: "Loving everything that increases me."

You could live like that all right, especially if you'd once felt, as he did, that every action you took was poisoning further the wellsprings of your life. It could be read, in fact, as a kind of boiled-down, idiosyncratic version of the third step of Alcoholics Anonymous – Made a decision to turn our will and our lives over to the care of God as we understood Him. It has the same faith in enlargement, in the possibility of benediction from oblique and unexpected sources.

On my last day in Port Angeles, I went out to Ocean View cemetery to visit Carver's grave. There were pines at the edge of the field, and beyond them the land dropped away, falling 400 feet or so to the water beneath. I could hear the waves moving very softly, a lush, lulling, impossibly rich sound. In September 1987 Carver was out there on his boat with a friend when they looked up and saw a group of people on the bluff. "I think they're planting somebody up there," he said, and turned his attention back to the sea. He'd been coughing all month but wouldn't know for another few weeks that there were malignant tumours in his lungs.

The sky was glazed with clouds, like curds and whey. I saw his headstone immediately. I recognised it from photographs: black marble, with the poem "Late Fragment" carved on it. It's a poem about love and self-acceptance; about gratitude and miracles. Carver once said he didn't believe in God, "but I have to believe in miracles and the possibility of resurrection. No question about that. Every day that I wake up, I'm glad to wake up."

I stood by that grave for a long time, thinking about alcohol, and the trouble it brings. There's a saying in AA that addiction isn't your fault but recovery is your responsibility. It sounds simple enough but making that step is about as easy as standing up and dancing on a sheet of black ice. In Cat on a Hot Tin Roof, Brick says to his dying father: "It's hard for me to understand how anybody could care if he lived or died or was dying or cared about anything but whether or not there was liquor left in the bottle."

Imagine feeling like that. And then imagine sitting down at your typewriter every morning, day after day, year after year. It was Cheever's words I thought of then. In 1969, when he was still in the thickets of his own addiction, he was asked if he felt godlike at the typewriter. What he answered seemed to me to sum up the ambiguity of writers and alcoholism, the difficulty of passing judgment on lives at once so troubled and so blessed. "No, I've never felt godlike," he said. "No, the sense is of one's total usefulness. We all have a power of control, it's part of our lives: we have it in love, in work that we love doing. It's a sense of ecstasy, as simple as that… In short, you've made sense of your life."

© Olivia Laing. This is an edited extract from The Trip to Echo Spring, published by Canongate