Music Theory Question

Hi Folks,

I was asked a question about being able to figure out the chords to a song

if you only know the melody and was hoping that someone could shed some 
light in how to figure this out.  For example, lets say, instead of trying

to figure out the key, and chords, you just have a melody line and want to

figure out which chords go with the melody line being sung, how do you 
figure that out?

Thanks