the first thing to do would be to know your notes, what key they are playing. this will shorten the list of possible chords to search for.
second,figure out notes from one phase, write the notes down and see what chords does these notes form in your key then try to play the chord over the song to see if it match. most of the times, you will find that there are more notes played, like AddChords and susChords. when you figure out the basic chord these notes can be easily introduced later on.
Of course this will take some time first, but with proper training and experience you will figure songs all out just by listening to them later on.