I've taken this from what I've heard of Glen Hansard and Marketa Irglova's version and 
posted on the site. I'm fairly sure it's right but there are bits where you can vary if 
wish.

You can play the F as a barre chord (133211) or you can play an F6 variation (x30210) 
roll your first finger onto the high F in the shape of F6 (x30211). When he strums F 
into the chorus he seems to hold the low E with his thumb. The strum for it is DDD UDUDUDU


Intro:
  C                   F                 C                  F
E----------0------------------1----0-------------0--------------------------|
B-1---3----------3----1---3-------------1---3---------3----1---1---1---1----|
G---0---0----0-----0----2---2---2----2-----0---0----0----0----2---2---2---2-|
D---------------------------------------------------------------------------|
A-3-------------------3-----------------3------------------3----------------|
E---------------------------------------------------------------------------|

Verse 1:
  C                   F                 C                  F
E----------0------------------1----0-------------0--------------------------|
B-1---3----------3----1---3-------------1---3---------3----1---1---1---1----|
G---0---0----0-----0----2---2---2----2-----0---0----0----0----2---2---2---2-|
D---------------------------------------------------------------------------|
A-3-------------------3-----------------3------------------3----------------|
E---------------------------------------------------------------------------|
 I don't know you     but I want you    all the more for that
  C                   F                 C                  F
E----------0------------------1----0-------------0--------------------------|
B-1---3----------3----1---3-------------1---3---------3----1---1---1---1----|
G---0---0----0-----0----2---2---2----2-----0---0----0----0----2---2---2---2-|
D---------------------------------------------------------------------------|
A-3-------------------3-----------------3------------------3----------------|
E---------------------------------------------------------------------------|
Words fall through me and always fool me and I can't react

Bridge:
  Am           G        F            G                 Am
E--------0--------------------1----------------------------|
B--------------3---1--0--------------3----1----0-----------|
G------2---2--------------2------2-----------------------2-|
D----------------------------------------------------------|
A--0---------------------------------------------------0---|
E--------------3--------1------------3---------------------|
   Games that ne-  ver a-mount to    more than they're meant


         G                F(strum)
E--0----------------------1----------------|
B--------3----1----0------1----------------|
G----2--------------------2----------------|
D-------------------------3----------------|
A-------------------------3----------------|
E--------3----------------1----------------|
   will play  them-selves out.

Chorus:

C                 F                 Am                   F
Take this sinking boat and point it home we've still got time
C                   F                 Am                    F
Raise your hopefull voice you had the choice you've made it known

Verse 2:

  C                   F                 C                  F
E----------0------------------1----0-------------0--------------------------|
B-1---3----------3----1---3-------------1---3---------3----1---1---1---1----|
G---0---0----0-----0----2---2---2----2-----0---0----0----0----2---2---2---2-|
D---------------------------------------------------------------------------|
A-3-------------------3-----------------3------------------3----------------|
E---------------------------------------------------------------------------|
  Fa- lling slow-ly   eyes that know me and I   can't go back

  C                   F                 C                  F
E----------0------------------1----0-------------0--------------------------|
B-1---3----------3----1---3-------------1---3---------3----1---1---1---1----|
G---0---0----0-----0----2---2---2----2-----0---0----0----0----2---2---2---2-|
D---------------------------------------------------------------------------|
A-3-------------------3-----------------3------------------3----------------|
E---------------------------------------------------------------------------|
  Moods that take me  and e-  rase me   and I'm painted black

Bridge:

Am           G        F            G                 Am
E--------0--------------------1----------------------------|
B--------------3---1--0--------------3----1----0-----------|
G------2---2--------------2------2-----------------------2-|
D----------------------------------------------------------|
A--0---------------------------------------------------0---|
E--------------3--------1------------3---------------------|
  You have     suffered enough and   warred with yourself

         G                F(strum)
E--0----------------------1----------------|
B--------3----1----0------1----------------|
G----2--------------------2----------------|
D-------------------------3----------------|
A-------------------------3----------------|
E--------3----------------1----------------|
   it's  time that you    wo-on

Chorus:

C                 F                 Am                   F
Take this sinking boat and point it home we've still got time
C                   F                 Am                    F
Raise your hopefull voice you had the choice you've made it known
C              F               Am             F
Falling slowly sing your me-lo-dy I'll sing a-long

he then strums the chorus a couple of times, strums F a few times and returns to the 
from the verse to end