Learn how to play power chords. Power chords are used by punk rock bands because of their ambiguity; they do not contain the third of the chord, only the root and fifth, so they cannot be classified by a quality such as major or minor. Play power chords on the guitar by placing your index finger on the low E or A string and your ring and pinky fingers on the A and D strings (if your index is on the E string) or the D and G strings (if your index is on the A string). Your ring and pinky fingers should be on the same fret, two frets up from the index finger; for example, if your index finger is on the fifth fret, your ring and pinky fingers are on the seventh fret. This chord shape can move anywhere up and down the neck.
Learn some riffs from your favorite punk rock songs. Classic punk rock songs include "Blitzkrieg Bop" by the Ramones and "Anarchy in the UK" by the Sex Pistols. These songs use power chords and are very characteristic of the punk rock style. Listening to punk rock songs and practicing them can give you more ideas for your own riffs.
Practice guitar techniques like strumming and palm muting. You can play chords with palm muting by placing the side of your palm just underneath your pinky finger against the strings while you strum the strings; this technique results in a chunky sound. You can also mute the strings with your fretting hand and strum the strings. Practice strum patterns in the punk rock style, which often consists of eight fast strums per chord. You can also try techniques like hammer-ons and pull-offs. Play hammer-ons by plucking the string once and "hammering" your finger onto another fret of the same string, so you end up hearing two notes with one pluck. Pull-offs follow a similar technique; instead of putting a finger down on another fret, you pull a finger off by slightly plucking the string with your fretting hand.
Study basic music theory. Most songs involve three chords, usually the I, IV and V chords. In the key of A, an A chord is I, D is IV and E is V. Pick a key and figure out the I, IV and V chords.
Choose the chords you want to use for your riff and make a strum pattern to go along with each chord. Use techniques like fast strumming and palm muting. Add hammer-ons and pull-offs for variety.