Palm-mute the open low E string. Rest the side of your picking hand on the bridge, so the flesh of your palm just touches the strings on the side of the pickups. Pick the low E string to hear a palm-muted note. Palm muting should be done liberally in metal guitar. Experiment with moving your hand closer to the neck and further away to get different sounds.
Play only down-strokes to get a crushing, attack sound into your riff. With down-strokes, you always hit the lower notes, and keep firm, brutal rhythm. Alternate picking is good for tremolo picking sections, but the majority of metal rhythm work should be played with only down-strokes. Fret a note and practice plucking fast, repeated down-strokes. Minimize the movement of your hand to increase speed.
Use power chords in your rhythm. Power chords are the bread-and-butter chords of heavy rock and metal. The power chord shape is the same regardless of the position on the guitar neck, but they can only be played on the E, A, D and G strings in this way. Choose a fret on either the E or A string and place your index finger on it. Put your ring finger on the next string down, two frets higher in position. Add your little finger onto the string below your ring finger, on the same fret. Play these three strings to hear a power chord. This position can be moved up and down the neck of the guitar to make different notes. If you tune in "drop D," you can play power chords on the D, A and D strings with one finger.
Construct a rhythm based around palm muting and power chords. A common technique in metal is to palm-mute the open low E string and accentuate that with power chords played at regular intervals. For example, "For Whom the Bell Tolls" by Metallica does this. "Enter Sandman" by Metallica is similar, with even, palm-muted strums leading up to a single, stabbed power chord.
Palm-mute the main riff for your rhythm section if you have one. The intro riff, played with palm muting, can often be turned into a suitable rhythm section for your verse or solo section. Alternatively, palm-mute the majority of it and release the muting for the riff's end or use the key notes in the main riff to construct a verse rhythm riff.