Seriously, I don't think it's fruitful to try to "work out" chords to a melody until one has either (a) studied some basic theory or (b) learned a few hundred songs with chords "included."
The (a) approach may actually be the faster of the two. But the (b) approach, the better one imho, will eventually fill your internal ear with the sound of various common chord sequences and how they fit with various melodies, to the point where it will become fairly obvious what chords belong in a given situation.
-Glenn