This is kind of amazing for someone who doesn't read a note of music
Paul McCartney on receiving an Honorary Fellowship to the Royal College of Music, 2017
None of the Beatles could read or write music. This was largely by choice. John, Paul and George all had opportunities to study music either at school or through private lesson. None got past the first few lessons.
Only Ringo certainly could genuinely claim to have been deprived of a musical education. Prolonged periods of ill health meant that his formal schooling was extremely sporadic. Even more than the others he relied on musical intuition.
In an interview Ringo once explained that time signatures 'were like ancient Egyptian to him when described in formal terms. He was baffled by the instruction to play 7/4 in the 'sun, sun, sun, here it comes' section Here Comes the Sun until it was practically demonstrated to him
All four had access to an instrument by adolescence - though in Ringo's Dickensian childhood this consisted of a toy drum delivered to his hospital bed. In fact
John was also in a church choir where he could have learned basic sight reading if so inclined (he wasn't).
How did they learn to play songs?
By watching other musicians play, listening to the records they liked and sharing practical technical tips with their peers. This is commonly referred to as 'playing by ear'.
The Beatles were what Hollywood composers called you 'hummers' - as in 'you hum the tune and I'll play it.' This relied on a very good 'ear' (ability to identify and reproduce the pitch).
Of course they needed to understand some fundamental musical concepts like keys, chord progression etc. This tended to happen on a piecemeal basis. Paul McCartney often tells how he and George across took a bus trip Liverpool to meet a guitarist who who could show them the B7 chord.
What about when classical musicians recorded with them?
Two words: George Martin. He wrote the string arrangements for Yesterday, Eleanor Rigby etc. He would then conduct the session players.
What happened when the began writing more musically complex songs?
Though Paul could communicate his musical ideas clearly. With John it was more
McCartney’s case is interesting because his innate musicality would have made it easy to pick up the basics. He could, for example, reel off the complex chord progressions in his own songs and yet claims that he could only see whether notes were going up and down from the scores presented to him by George Martin.
I think there was something more complex going on. The Beatles learned music by ear and it was natural for them to play that way. When George Martin brought in orchestral arrangement (for Yesterday, Eleanor Rigby etc) the classical players worked from scores - but often under McCartney’s direction. Like a foreign football manager struggling with an unfamiliar tongue he did not want to express himself clumsily and relied on an interpreter to communicate (usually Martin). The power balance was better maintained if he didn’t rather than couldn’t read music.
Did the lack of formal training limit them?
Other musicians like Ginger Baker scoffed at The Beatles rudimentary technical skills. I think this misses the point - McCartney just took a different approach. Golden Slumbers, for example, was famously inspired by seeing his younger niece’s piano music laid out for a lesson. Paul looked at the notes and then imagined the tune they might represent.
They don’t teach that in composition class.