Tuning: Drop Db
Tabbed By Shotgun Joe
Album: Mezmerize (BUY IT NOW!)
This is just the way I play it, and it sounds good, so it could work for you.
.=Palm Mute
P=Pick Scrape
Intro Part 1(x2)
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-12-0-12-0-12-0-12-0-13--12-0-12-0-12-0-12-0-13----|

Intro Part 2
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12--0000000000000000-------------------------------|
12--0000000000000000-------------------------------|
12--0000000000000000-12-0-12-0-12-0-12-0-13--------|
    ................

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12--0000000000000000--13--15--13-------------------|
12--0000000000000000--13--15--13-------------------|
12--0000000000000000--13--15--13-------------------|
    ................

Play the top part of Part 2 again, then:
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12--0000000000000000---13-15-13--13-15-13----------|
12--0000000000000000---13-15-13--13-15-13----------|
12--0000000000000000-P-13-15-13--13-15-13----------|
    ................

Intro Part 3 is basically the same as Part 2, it is played the same amount of times, 
of just thrashing at the strings with the palm muted 0's half the amount of times you play 
and play everything else the same.

Verse Part 1 (x2)
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-12-13-15-13-12-13-15-13-12-13-15-13-12-13-15-13------|

Verse Part 2 (x4)
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12-12-12-12-12-12-13-|
12-12-12-12-12-12-13-|
12-12-12-12-12-12-13-|

Chorus Part 1
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----1--------5--------0--------3-------------------------|
----1--------5--------0--------3-------------------------|
----1--------5--------0--------3-------------------------|

Chorus Part 2
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-1--1--1-1-1-1--5--5--5-5-5-5--0--0--0-0-0-0--3--3--3-3-3-3-|
-1--1--1-1-1-1--5--5--5-5-5-5--0--0--0-0-0-0--3--3--3-3-3-3-|
-1--1--1-1-1-1--5--5--5-5-5-5--0--0--0-0-0-0--3--3--3-3-3-3-|

Bridge (x2)
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---1---------5---------0---------3-----------------------|
--1-1-(x4)--5-5-(x4)--0-0-(x4)--3-3(x4)------------------|
-1---------5---------0---------3-------------------------|

Order
Intro Part 1
Intro Part 2
Intro Part 3
Verse Part 1
Verse Part 2
Verse Part 1
Verse Part 2
Chorus Part 1 (x2)
Verse Part 1
Verse Part 2
Verse Part 1
Verse Part 2
Chorus Part 1 (x2, with extra 3rd fret stuff at the end)
Bridge
Intro Part 2
Intro Part 3
Chorus Part 1
Chorus Part 2
Intro Part 3