We've done the song in Drop D so it'll be easier for you to retune without upsetting your guitar too much. If you are in standard tuning, just play the middle D string (open) and tune down your Low E string (2 frets worth) to match it:
Drop D Tuning: Low D : A : D : G : B : E
The band actually play in Drop C which is exactly the same tuning, except each string is dropped by a further 2 notes. Learn it as we show here, and drop everything to C if you wish, just be very careful with rebalancing your neck tension or bad things may happen to your guitar.
The song is very fast, and you will need to practice to get to full speed. However, if you take each riff slowly, you'll see that it's not actually that difficult to play. Developing full speed will take time, because you need to alternate pick very fast and skip across strings without missing a beat. The way to practice this is to get it right slowly first, then work at building your speed afterwards. It will take time, but once you have the basic alternate picking technique down, other cool metal songs which use the same techniques will become easier to learn too (e.g. Metallica, Megadeth, Slayer, Sepultura etc).
Here we look at the main guitar. This is all you need to play through from top to tail. There is a second guitar too which mostly plays the same riffs, does the odd harmony, and backs up the solo.
Main Riff - This is actually a fairly short riff, repeated lots. It always repeats just after this little descending lick. The trick here is to switch between palm muting and open note strikes without breaking the flow of the riff. Although it's fast, take your time and get it right first. Go as slow as you need, always build the speed last.
Second Riff - This riff is a little easier to play. Again, it's quite short and repetitive.
Third Riff - This is the easiest part of the whole song. It's just single notes constantly alternate picked. There is a second guitar also playing a similar thing, just with different notes (for harmony) - see this ActionTab.
Lead Melody - Start with a pickslide (scrape the edge of your pick down the length of 2 strings). Then bang the Low D5 chord and launch into the pleasant little lead melody. It is a repeating lick, and halfway through Guitar 2 comes in with a harmony.
Pre-Solo Riff - Starts off easy enough but gets much faster. You need to fret across 2 strings with your fingers and alternate pick both at the same time. As usual, you simple have to go slow at first and build the speed. It will take practice to get tight with this technique.
Solo - This is a great metal solo, it uses many typical lead licks but in a good way. It's not easy, or for beginners. However, it's worth taking a look at to see how he combines various solo techniques. Here's some points of interest for you:
Scale Run - A technique where you run through a scale according to a repeating step pattern (We explain these here in Core Skills section).
Fingertapping - To get a very fast flurry of notes. Whole section on this in the Core Skills.
Descending slide Run - Descending through a repeating pattern, using slides between positions. Discussed here and here. Ends with a low whammy bar on the D string and a pinch harmonic (he plays this differently live).
Triad lick - Here he uses triads (3 notes that make up chords). However, he plays the notes from these triads in a 'neo-classical' way. The notes are rapidly played using pull offs and a certain repeating pattern. Listen / Watch and you'll get it. You need the pull offs in this lick to sound cleanly. Practice the first triad until you get the hang of it, then work on the next triad (the picking hand does the same stuff, only the fretboard hand changes notes). Then work on shifting hand positions quickly between the different triads last.