Start by trying to hum what you hear. Then try to find the melody on the guitar. What I mean by that is try to find the notes your are humming.
Once this is done WRITE THEM DOWN lol (or record them if you can)
I've lost many great melodies because of that. Sometimes it's a flash and if you don't write them down, you quickly forget them.
When you've wrote them down, look a the notes and try to play the chords of those notes. Play all chords at first, then as you play around you'll end up concentrating on the chords you like and the chord progression that speaks to you.
You could also try to find the Key the melody is using then apply some of the most common chord progression but I personally prefer going by ear at first. If I'm stuck I'll open the theory book.
This is a very good thread in which Christopher explains how to find the key of a melody or song.
http://www.guitartricks.com/forum/showthread.php?t=23887
Good luck