A rollicking rush on guitar is followed by the line, "I don't know why I love you like I do", sung with something between a hollow laugh and a stab of pain; and after one minute and 37 seconds it is over. Side one, track one, of the first album by Bob Dylan, the most elusive, talented and influential American performer and poet of the 20th century.

There follows a classic talkin' blues that sounds like the work of an old hand, but expresses the awe of a young man on arrival in New York – then the voice, more vehement, intensifies for a searing third track that strokes the listener's every exposed nerve that little too roughly – a spiritual called In My Time of Dyin', with the singer's girlfriend's lipstick tube used to try to imitate the slide guitar of blues wizard Robert Johnson.

The album – entitled Bob Dylan – was released half a century ago (19 March 1962) , by a 20-year-old from Minnesota who had arrived in Manhattan the previous year, aboard a freight train. It had taken him two months to get much further than Times Square, before trying his luck in places like "an unusual beer and wine place on 3rd Street… now called Cafe Bizarre", as Dylan would later recall. "The patrons were mostly workingmen who sat around laughing, cussing, eating red meat, talking pussy… Talent scouts," he wrote, "didn't come to those dens."

Dylan finally arrived in the creative ferment of Greenwich Village with burning ambition to match it – "impatient to be seen, to impress important people, to learn", as Robert Shelton, the music critic who became Dylan's biographer, puts it. In the city Dylan described as "mysterious" but "capital of the world", he pressed himself through the doors of the coffee houses and folk clubs: the Commons, the Wha', The Gaslight – and Gerde's Folk City.

"I was there to find the singers," Dylan would write, "the ones I'd heard on record – Dave Van Ronk, Peggy Seeger, Ed McCurdy, Sonny Terry and Brownie McGhee." Dylan's first album was released in the same year that the Beatles recorded Love Me Do; Jimi Hendrix was still serving in the 101st Airborne Division; Frank Sinatra cut an album with Count Basie; and Dmitri Shostakovich premiered his 13th Symphony, with two more to go and 13 years longer to live. "Although only 20 years old," read a review of Bob Dylan in the New York Times, "Dylan is one of the most distinctive stylists to play in a Manhattan cabaret in months."

Throughout the 50 years since then, Dylan has maintained his enigma, which is all the more remarkable for having written what is regarded as an intimate autobiography, Chronicles.

His girlfriend Suze Rotolo – photographed on Dylan's arm for the cover of his second album, The Freewheelin' Bob Dylan – wrote a memoir recounting the depths of Dylan's determination to stay mysterious at that time: he span her a yarn about having been abandoned as a child in New Mexico. Rotolo had suspicions about his "Welsh name" and prised his real one, Zimmerman, out of him at the apartment they would eventually share on West 4th Street (though she liked calling him Boo Radley after the couple went to see To Kill a Mockingbird).

But 2004's Chronicles does at least allow us to quote Dylan on himself after all the decades of elliptical responses and riddles with which he baffled interviewers. Most important, we can read his own account of coming to know the man who inspired this first album more than anyone: the hobo father and political conscience of American folk, Woody Guthrie. Nothing on the album is written by Guthrie, but the traditionals are sung as he might have performed them.

Dylan recalls buying Guthrie Raleigh cigarettes to smoke in hospital and singing Tom Joad to its author during long afternoons by his deathbed. Only two songs on the first album are written by Dylan: Talkin' New York and Song to Woody – the former adapts a Guthrie talkin' blues and the latter is a homage. Dylan's reasoning for this is disarmingly frank: "I can't say when it occurred to me to write my own songs. I couldn't have come up with anything comparable or halfway close to the folk song lyrics I was singing to define the way I felt about the world… Folk songs played in my head, folk songs are the underground story."

Playing at Folk City, Dylan won admirers and jealous adversaries. Joan Baez would recall: "He looked like an urban hillbilly… bouncing from foot to foot, he seemed dwarfed by the guitar… He spat out the words to his own songs. They were original and refreshing, if blunt and jagged. He was absurd, new and grubby beyond words… but captivating."

However, Dylan failed to turn his success in the cellars into a recording deal – he was rejected by Elektra, Folkways and Vanguard. Then he met John Hammond, at a rehearsal in an apartment rented by Baez's sister, Mimi Fariña, and her husband Richard.

Hammond was the genius who produced Dylan's first album, adding the young singer to the list of those he had nurtured, which included Billie Holiday, Charlie Christian, Bessie Smith and Count Basie.

By November 1961, Hammond was ready to move his new talent into Columbia's Studio A on Seventh Avenue. "I signed him on the spot," he once recalled. "We made our first album almost immediately. His guitar playing, let us say charitably, was rudimentary, and his harmonica was barely passable, but he had a good sound and a point of view and an idea. He was very disenchanted with the social system. I encouraged him to put all his hostility on tape, because I figured this was the way, really, to get to the true Bob Dylan."

Some of the songs were recorded in two takes, such was Dylan's germinal feel for the music, the folk, the blues. The only problems arose from Dylan popping his Ps, too close to the mike.

The immediately astonishing impact of the album, by any measure, is the contrast between the image of the unsmiling but fresh-faced lad in his cap and the depth of feeling and range in the singing between love, rage, sorrow and a fixation with death. The core of the album is Fixin' To Die, sung as though he were pleading for the life he is about to lose, such is Dylan's understanding of the intentions of its author, the great Delta blues master Booker T Washington – aka "Bukka" – White.

And so it continued: the lighter guitar touch on Baby Let Me Follow You Down, heralding the mighty ballads to come, a definitive claim on House of the Rising Sun and Elizabeth Cotten's Freight Train Blues – a choice worth noting not just for the lore of the American railroad and whistle of iron snakes winding through perpetuity, but also Dylan's own reflection that "I'd seen and heard trains from my earliest childhood days and the sight and sound of them always made me feel secure".

As ever, there is humour, too. Baez, Dylan's lover in the period immediately after the album, wrote that "his humour was dry, private, and splendid".

The estimable British writer on Dylan, Michael Gray, argues interestingly that the real value of the album is not only that it showed "more than a hint of a highly distinctive vision", but also "served as a fine corrective for Greenwich Village: it was the opposite of effete," he says, "in the context of what was happening at the time – American folk culture all but obliterated, and a stagnating 'folk' cult established as if in its place."

In Chronicles, we have Dylan's recollection of the books he devoured off other people's shelves during the time he made this record, which illuminate those to follow: Shelley, Poe, Faulkner, Gogol, The White Goddess by Robert Graves, whom he would later meet in London; "Balzac is hilarious," writes Dylan – and there is his "morbid fascination" with Von Clausewitz's writing on warfare. Books that can be said to play their part among the myriad influences on what was to follow – indeed, once Dylan had embarked along the creative road he would take from Bob Dylan onwards, it was a while before he returned to the album in his core performing repertoire.

"Sometimes you just want to do things your way, want to see for yourself what lies behind the misty curtain," he wrote. "You have to know and understand something, and then go past the vernacular."

Half a century ago though, the vernacular had a narrative and poetry of its own. But in his review for the New York Times, Shelton observed that, despite moments of "off-target melodrama", Dylan's "highly personalised approach towards folk song is still evolving".