Here's the main progression that appears in the song, it's the one heard most out of the four different progressions played throughout the song. This is a very common chord progression, heard in many styles of popular music. It's an 8 bar phrase and goes like this:

I Ab(add9)

VI Fmin(add9)

IV Db(add9)

V Eb(add9)

Then back to the one chord, Ab(add9). The turnaround varies between the one and the VI chord, depending on where you are in the song.

With your right hand, you want to get a steady 1/8th note palm muted rhythm going. Don't lock down on the bridge with your right hand because you want to be able to swell out of the palm mute and let the chorus breathe a little bit here and there, when the dynamics need to go up or down. You'll be using alternate picking, and once you're playing it tight you'll notice how the delay is helping the groove and makes it sound really cool.