I've seen this tabbed wrong on a few sites (including ninebullets.org, which has a lot 
DBT tabs)

The chord progression is a simple Am, F, G, back to Am throughout, but with some
of notes

I play the chords like so:

Am  x-0-2-2-1-x-|
F   x-x-3-2-1-x-|
G   x-x-5-4-3-x-|

During the Am and F, add and remove the 2nd string, 3rd fret (D) as per the picking
in the song (it's hard to tab...just listen for it)

During the G, you can pull off the 2nd string and play it open (for a B) then hammer 
on.

Intro: Am

Verses:
        F                                 G
When I saw her standing there, with her bright eyes and shining hair

        Am
She was looking back at me


and so on throughout