John, Paul, George and Ringo

Lennon met McCartney on July 6, 1957 at the annual St. Peter's Woolton Parish Church Garden Fete. Lennon was in a skiffle group called The Quarry Men who were performing at the event.
The Quarrymen as recorded on that fateful day- July 6, 1957 (press play twice to listen)
Lennon was impressed by McCartney as he knew the words to several rock 'n' roll songs (Lennon would just make his own words up), and because he taught him some guitar chords (Lennon only knew the banjo chords taught to him by his mother Julia).
McCartney subsequently joined the band,and brought Harrison along soon after, on February 6, 1958.
After a brief split, The Quarry Men regrouped in 1960 as The Fabulous Silver Beatles, later shortened to The Beatles. Pete Best, who had played occasionally with The Quarry Men, was auditioned on August 12th, 1960. Four days later, the group (with new member Pete Best) left for Hamburg.
Hamburg was a wild place for the young men. They were featured at the Indra, a small club where they were playing to Germans who often did not understand English.
They were uninhibited on stage, drinking alcohol, sometimes goading the crowd and acting unruly, but such was the club's atmosphere.
The Beatles playing together in Hamburg had the group becoming more tight-knit, better musicians and better showmen. When The Beatles were just about to switch to a bigger, more popular club, The Top Ten Club, Harrison was deported for being underage and they returned to Liverpool.
In March 1961, The Beatles played their first gig at Liverpool's 'Cavern Club' before returning to the lucrative Hamburg scene with a now legal Harrison. During their stay in Germany they were hired by Bert Kaempfert to record backing for the singer Tony Sheridan. A single, "My Bonnie", was released in Germany on the Polydor label in August 1961, credited to Tony Sheridan and the Beat Boys. It was The Beatles' first commercial release.
In the Spring of 1961, while still in Hamburg, Sutcliffe decided to leave the band in order to concentrate on his art studies. While Sutcliffe had had little musical impact on the group, he had influenced their appearance and sense of style. McCartney, who had been playing guitar, replaced him on bass.
On December 10, 1961, Brian Epstein agreed to become the band's full-time manager, after receiving requests for the band's music two months earlier in his record store ("My Bonnie by The Beatles" — Epstein couldn't find it) and watching them perform at the Cavern Club on November 9, 1961.
Epstein arranged for The Beatles to audition for Decca Records on January 1, 1962. Decca, in one of the most embarrassing business decisions in music history, rejected the band, on the grounds that guitar music was "on the way out". The Decca audition has subsequently accumulated significant legend.
The Beatles auditioned for EMI's Parlophone label on June 6, 1962. George Martin, who was at first unimpressed by the band's demos, liked them as people when he met them, and they were signed. Not only did he feel that they had musical talent, but he also felt that their wit and humor made them extremely "likeable."
Martin did have a problem with Best however, whom he criticised for not being able to keep time. For this and other reasons, The Beatles let Best go on August 16, 1962, although it was left to Brian Epstein to tell him. They immediately asked Starr, whom they had met and even performed with previously, to join the band permanently.
Source: http://en.wikipedia.org/wiki/History_of_The_Beatles