Palm muting gives you the tight, chunky chug used in rock and metal rhythm guitar. Rest the side of your picking hand, just below the little finger, lightly on the strings right where they leave the bridge saddles. Then pick as normal.
Too far forward and the note goes dead and pitchless; too far back on the bridge and there's no mute at all. Move your hand a few millimeters at a time until you hear a short "chuck" that still has a clear pitch.
The riff is in E minor on the low E string: open E, G at fret 3 (middle or ring finger), A at fret 5, B at fret 7. Keep the mute on for every note.
Use downstrokes for the eighth notes; they sound heavier and more even. For the sixteenths, switch to down-up alternate picking.
The most common mistake is the mute drifting as you play: the palm creeps forward and the notes get muddy, or lifts off on the fretted notes. Check by watching your hand for a few loops, then by ear.