Awesome song, awesome band, this song is fairly easy if you can alternate pick and 
use pinch harmonics to add that dave navarro effect

Key:
h/p hammer on/ pull off
. palm mute
{3} pinch harmonic
7/3,3/7 slide
b/r bend/release
v vibrato
\\\\\ tremolo picking

Intro/Chorus
e|----0---0-------0---0-----0---0---------------------------|
b|-------------/3---3---3-----------------------------------|
G|--2---2---2--/4---------2---2---2-----2-2-------------{9}-|  x1
D|--2----------/5---------2-------------2-2-----------------|
A|--0---------------------0-------------0-0-3-3-3-3-3-3-----|
E|----------------------------------12/---------------------|
                                            . . . . . .
Main Riff/Verse:
e|----------------------------------------|
b|---------------------6-4----------------|
G|---------------------6-4----------------|  x8
D|----------------------------------------|
A|----------------------------------------|
E|-0-2-2-2-2-2-2-2-2-2--------------------|
     . . . . . . . . .

Chorus x1
Main Riff/Verse x8
Chorus x1

Solo:
e|-------------------------------------------------------------|
b|-17b-17b---14-17-14-16-14---14-17-14-16-14---14-14b----------|
G|-16b-16b-16---------------16---------------16-------16-16-14v|
D|-------------------------------------------------------------|
A|-------------------------------------------------------------|
E|-------------------------------------------------------------|

e|-16b-14-14-----14------14-----14-----14-----14------------|
b|-----------17b----14h17--14h17--14h17--14h17--------------|
G|-----------------------------------------------16brh14----|
D|------------------------------------------------------16v/|
A|----------------------------------------------------------|
E|----------------------------------------------------------|

e|--------------------------------------------------------------------------|
b|----------------------------------------------------5---5---5----5---5---5|
G|-4b-{4b}-2h4-2-2---2--------2h3--------------2h3-4/6-4/6-4/6-4/6--4/6-4/6-|
D|-----------------4---4p2-4v-----4p2---2h4-4-------------------------------|
A|-----------------------------------2h4------------------------------------|
E|--------------------------------------------------------------------------|

e|----------------------------|
b|-5p4------------------------|
G|-----3p2--------------------|
D|---------4vvv---------------|
A|----------------------------|
E|----------------------------|

Chorus x1

Solo:
e|----------------------------------------|
b|----------------------2-x-x-2-2-4-4-4-4-|
G|-4v-4v-4v-{4br}p2-----2-x-x-2-2-4-4-4-4-|
D|------------------{4}-------------------|
A|----------------------------------------|
E|----------------------------------------|

e|-----------9-12p9-12p9-10\\\\\----------|
b|---------12-----------------------------|
G|-{4}/16v--------------------------------|
D|----------------------------------------|
A|----------------------------------------|
E|----------------------------------------|

e|----------------------------------------|
b|-17b--17b---------------14--------------|
G|-----------14v-------16-----------------|
D|----------------16v---------------------|
A|----------------------------------------|
E|----------------------------------------|

e|----------------------------------------|
b|-17p14--14-17p14--14-17p14--14-17p14-14-|
G|------16--------16--------16-------16---|
D|----------------------------------------|
A|----------------------------------------|
E|----------------------------------------|

e|-14p12-14p12-14----14p12----------------|
b|----------------14-------14h15-15\\\----|
G|----------------------------------------|
D|----------------------------------------|
A|----------------------------------------|
E|----------------------------------------|

Chorus x1

Outro
e|-------------|
b|-------------|
G|-------------|
D|-------------|
A|-------------|
E|-0-2-2--0-2--|
   . . .  . .