In the start of the song you can hear a bell like 
sound. Try to recreate this with harmonics on the 
12th fret of the high e-string. 
(Kjartan uses a sort of device to make this sound)

Throughout the whole song the same chords go over 
and over, except in the climax.

Play these chords for the basic progression:

  E  Dadd9  C#m7  Asus2

At first Jóonsi, plays some harmonics over the 7th fret, 
and all over the guitar (with his bow). 
Just improvise like he does. The intro will 
then be like this:

(on the low e-string, as usual)

|E-|-14-|-15-|-14-|-12-| two times
except the second time, it ends on a B note |-19-|

The timing is easy to catch, listening to the record.

E            Dadd9    C#m7    Asus2      
ég er kominn aftur (á ný) inn í þig 
     E               Dadd9     C#m7           Asus2   
(það er) svo gott að vera (hér til) en stoppa stutt við
E          Dadd9       C#m7      Asus2        
ég flýt um í neðansjávar hýði (á hóteli)  
E           Dadd9        C#m7       Asus2 
beintengdur við rafmagnstöfluna (og nærist)
  
  E  Dadd9  C#m7  Asus2 
tju         tju            (two times)

E        Dadd9       C#m7        Asus2
en biðin gerir (mig leiðan) brot hættan 
E      Dadd9         C#m7          Asus2
sparka frá mér (og kall á) verð að fara hjálp
 

 E  Dadd9  C#m7  Asus2
tju tju    tju   tju    (8 times)   
bm              A         E
ég spring út og friðurinn í loft upp
E  Dadd9    C#m7  Asus2
(baðaður    nýju  ljosi
E             Dadd9  C#m7 Asus2
ég græt og ég græt   aftengdur)
E       Dadd9 C#m7  Asus2
ónýttur heili settur á brjóst
E     Dadd9 C#m7     Asus2
og mataður af svefn-g-englum

 E  Dadd9  C#m7  Asus2
tju tju    tju   tju          

The chords:
 
   E  Dadd9 C#m7 Asus2 Bm   A
|e-0---0-----0-----0----2---0-|
|B-0---3-----0-----0----3---2-|
|G-4---2-----6-----2----4---2-|
|D-6---4-----2-----2----4---2-|
|A-7---5-----4-----0----2---0-|
|E-0---¤-----¤-----¤----¤---¤-|

if you want it easier, just play the
normal Dadd9 and C#m7 chords.

 Dadd9  C#m7
|e-0(2)--4----
|B-3(5)--5----
|G-2-----6----
|D-0-----6----
|A-¤-----4----
|E-¤-----¤----