They were all from Liverpool originally. George Harrison and Paul McCartney took the same bus to school, and found out they had music and guitars in common.
In 1956, Paul introduced George to a band called the Quarrymen which John Lennon sang in. George was only 14 at the time and not old enough to join the group. But a few times he filled in for the regular guitarist and gradually became a member of the band.
The Quarrymen became The Beatles, performing regularly at the Cavern Club in Liverpool, and within another four years the foursome became worldwide superstars.