Here is an interesting recent PW thread on playing by ear. The response that really caught my eye was from Gyro. Below I quote in full what he wrote. Something simple to start with and to build on. No music theory needed! 🙂

Practical by-ear playing is not that difficult. Starting on the C one octave below middle C, and going up the white keys, play the 7 four-note chords using every other white key:

CEGB, DFAC, EGBD, FACE, GBDF, ACEG, BDFA.

This is the foundation upon which all chords for by-ear playing are built. (In some songs, particularly older songs and rock and country oldies, sometimes only 3-note chords are used: CEG, DFA, EGB, etc.)

Note that each of the 4-note chords above can easily slip into a second chord without changing the first two notes: for example, CEGB can slip easily into CEFA, or CEGA, etc. This is…