They call it "three chord theory" but I don't know what the theory is. What it comes down to is that any note in a tune in a particular key is going to be in one of the three chords, so if you play a chord with the relevant note in it, it'll sound right. Except in some tunes you use a different set of chords because you are using a different scale...

In practice what you do is - what I do anyway - is somehow get a feeling that you need to play a different chord when the tune turns, and you know which one. Once you know what key it is, the choice is small enough. Damned if I know how you learn to do it - just try playing along with people (or along with records - and you find you've leaned how to do it. For some odd reason I found it a lot easier learning to do it along with people than along with records, even when there was no one playing an instrument that I could follow for the chords.