I'm not well versed in this, but I have the basics down: start by finding the bass notes, and add the melody on top. Most of the time the a musical phrase will end on the note that's in the key of the song.
Combine the bass note with the third and fifth, and you're already halfway there...
Typical chord combinations are in the 1-4-5-6, so when the key is in C, for the first chord (I) you start on the C, skip one, E, skip one and then G. These 3 notes compose the first chord. To get the second chord, just move your fingers one key to the right.
A major scale in C contains the following chords if you move your 1-3-5 grip one key to the right each time:
- I: C (C-E-G)
- ii: Dm (D-F-A)
- iii: Em (E-G-B)
- IV: F (F-A-C)
- V: G (G-B-D)
- vi: Am (A-C-E)
- vii: Bdim (B-D-F)
Capital roman numerals indicate major chords (happy-ish), lowercase indicate minor (sad-ish).
Just try a few combos of I, IV, V and vi with your right hand, while hitting the first note of the chord with your bass.
You will instantly come to a few recognisable tunes.
Up next is transposing scales: move every note two half steps up to get to a major scale in the key of D for example.
Another handy trick is inversions: look at the individual notes in a chord and when switching from one chord to another, minimize have movement by playing some of the notes an octave higher or lower.
This is just the start, but it should help you a long way to play list of the simple pop songs.