To switch to palm muting, put the edge of your picking hand on the strings near the bridge, in order to slightly muffle them there.
And while remaining in this position, pick the strings with a plectrum as usual, and that's all the trick ;)
Experiment with various amounts of pressure, that the heel of the picking hand puts on the strings, as well as with closeness of this hand to the bridge, and find what sounds best for you.
In guitar tabs palm mutes are indicated by P.M. abbreviation. If there's a series of palm mutes, a dotted line right after the P.M. shows till where it goes. When the dotted line ends you need to open up palm mute and play in a regular position.
Now let's move on to guitar riffs!
Pay attention that in the second part of the riff, each first chord in a bar is played without palm muting, the contrast of muted and not muted notes makes the riffs sound more interesting than if they would be played just with plain muffled tone.
Pay attention that power chords in this phrase consist of three notes, where the highest note, merely copy of the root note located octave higher. This trick allows to get more fat distorted sound out of guitar.
This riff perfectly connects into a theme, with the following riff #4. Practice over each riff separately, till it comes accurately, and next play one after another as a whole piece.
Note that on the repetition I play the riff a bit differently,on the
4th bar I one more time play the 3rd one, and finish up the phrase
with A power chord.
Also check out "Metal with Dennis" video lesson series that covers the palm mute along with slide guitar technique.
When you'll feel ready to move on, jump to the next lesson - 12 Bar Blues Progression where I've put a couple of cool blues riffs and introduced shuffle rhythm.