This rhythm guitar part is played by Adrian Smith. Generally speaking, it is actually harder to play than the Lead guitar played by Dave Murray - except for the solo. So you should start with that ActionTab instead, and then learn this one if you want to.
For the most part, this rhythm guitar does exactly what you'd expect. It provides the main backing for the song. Adrian's rhythms are much more intricate than Dave's in this song, which is why it's harder to play. Also, there are places where he plays harmonies along with the lead.
Intro - Start by constantly palm muting the D note. Dave starts playing his lead riffs over this, and after a while Adrian switches to play similar riffs too. They are basically the same as Dave's riffs, except they finish with palm muting chords etc (while Dave just hangs onto a single note each time). What Adrian plays here is actually more varied and intricate than Dave, even though it is just rhythm guitar.
Verse - Technically speaking, Adrian switches to lead guitar here while Dave chugs out powerchord rhythms. Adrian switches to a slightly cleaner guitar sound and picks out notes for the following chord shapes to compliment Dave's backing chords:
D minor - C sus2 - G minor - Bb5 - C5 (repeat)
Harmony 1 - In the middle of the verses both guitars play a little harmony. This is the melody played by Adrian, meanwhile Dave plays a similar melody underneath. 2 or more (different) melodies played together make a harmony.
Harmony 2 - After the next verse, harmony 1 is played again. However, afterwards it is dropped by 2 frets. It's the exact same thing, just played lower.
Bridge - Although this is essentially a simple sequence of powerchord changes, it is a bit trickier than it looks. It is not the same as what Dave plays, but it is similar. This part is meant to be played fast, and the main difficulty here is in getting the finger changes on the fretboard done in time. Halfway through the bridge, Adrian switches to play this melody.
Solo Backing - While Dave does the solo, Adrian plays this repetitive E major scale lick. Then he reverts to the same riffs as the intro, starting at fret 7 this time.
The only other different guitar parts in the song are the last half of the final bridge. It's the same as the first bridge melody, played just before - except everything is lower by 2 frets.
Also, the Outro is just the same as the second half of the intro, ending with this little lick.