This song is recorded in C tuning (4 frets down) by Arch Enemy, but we're doing it in standard E tuning to save you re-tuning / ruining your guitar. It's the right way to play the song, just sounds a bit higher due to the higher tuning.
Any Arch Enemy fan will know that the band like to play very fast. So bear that in mind when I say that this is one of their 'easier' songs. To play it you need to develop fast palm muted picking (alternate up/down strokes) and be able to throw in open picked notes / chords. Go to the Picking Section in Core skills for more on that stuff.
Otherwise, just practice the first (verse riff) lots until you develop the speed and control needed for that technique. It takes some dedicated practice, but once you can do it the world of fast metal riffs will open up for you. Go as slow as you need to at first, but start speeding it up as soon as you can get the picking consistent. The more you do that, the faster you will get it, with fewer mistakes. Music like this is all about precision playing. Believe it or not, tight timing and control is sometimes easier when playing at full speed than at slower paces.
There are 2 guitars for the song (played by brothers Michael and Chris Amott). This is Michael's guitar and definitely the main one to learn for all the best song riffs. He also does the only solo in the song. Rather unusually, Chris takes more of a rhythm guitar role in the song.
Main (Verse) Riff - Short and repetitive. This is a great riff for practicing your speed metal techniques. As stated above, work on getting consistent alternate pick strokes first, then build your speed. All the notes on the Low E string are palm-muted except for this 3 note lick. Sometimes they don't play that 3 note lick, they just continue palm-muting - like here. If you are struggling with that little 3 note lick, play this riff variation instead. Come back to to the lick later.
Riff 2 - This little riff involves switching across by 1 string and playing pull-offs. The palm muted rhythm has a couple of gaps. Notice that after 2 times Michael shifts up to play the pull offs slightly higher (although the basic riff remains exactly the same). Meanwhile Chris continues playing the original riff.
Just keep alternating between these riffs until the chorus...
Chorus - This is a fast octave chord sequence played while Chris does backing powerchords. It's the easiest part of the song, and requires muting between bursts of 4 strums each time a chord is played.
The middle and last chorus / outro are more of the same, except more octave chords are added afterwards.
Watch out for this Last Verse Riff variation. It's almost exactly the same as the normal riff, except that this note is played 1 note sooner. That means playing 5 palm muted notes afterwards instead of 4 to compensate. Chris continues this riff while Michael does the solo.