BigDaddy, there are often more than one set of chords that will work for a song but the good old 3 chord trick is always worth a try for songs in major keys.

John In Kansas noted it in an earlier post. In this case, we know the tune is in A so A is the 1 chord, D is 4 and E is 5 and these will be the most likely 3 chords that crop up in A major.

You can pretty well get there by trial and error - when you hear the chord no longer fits - try one of the others which may well work. After a while, you reach a stage where your ear will tell you just by listening to the melody which chord to change to and you'll probably start "hearing" some minor chords too.

Clever people than me can hear and put all sorts of chords in but that is a basic start that seems to work for a few of us.

Jon