The chords are fairly simple. One thing he does a few times in the song (and loads of times in his own songs) is play the F chord with the G string open, then hammer on at the second fret. He does a similar thing with the G chord. This time the A string is left open then hammered on.
I’ve included two versions of Am in the song (one with the A string open and one with it at the third fret). He always uses the third fret version on the C – Am change that you hear at the beginning. He throws in the easier version on a few occasions towards the end.
Kudos to Leonard Cohen for making my job easier by describing the chords in the lyrics. Why can’t all songwriters be so helpful?
Any simple 3/4 pattern will see you through. A good one to start out with is:
d – d u d –