Study the classic punk rock bands. Musicians develop their skills, chops and ideas by emulating their musical heroes. This is as true for punk rock musicians as for any musician. For example, the Sex Pistols are heavily influenced by the New York Dolls and wanted to play music like their heroes. The Sex Pistols don't sound much like the Dolls, but emulating the Dolls got the ball rolling. Study the punk music of Iggy and the Stooges, the Sex Pistols, the Clash, the Ramones and other bands. The first step in creating your own punk music is to listen to the classics, but the goal is to create your own voice.
Find or form a group of like-minded colleagues. It is difficult to make punk music on your own. The basic requirements for punk music are guitar, bass, drums, a singer with an attitude and ample volume. Get involved in the local music scene. Frequent local clubs and house parties that feature punk music. You may find like minded souls at such places who are interested in forming a band. Place an ad in local musician weekly newspapers describing the type of band and the type of musicians you are looking for. Extend your search to online searches. Doing a "musicians wanted" search online provides a broader range of potential band mates.
Create your own songs. The first step in writing your own punk song is finding a interesting power chord combination or guitar riff. Punk songs don't use complicated chords. The basic component is a power chord, using lots of distortion, played with all downstrokes. A power chord is played on the sixth, fifth and four strings of the guitar. Downstrokes are played by striking the strings in a downward motion with the guitar pick. Playing the chord with all downstrokes produces a more aggressive sound than the more typical guitar approach that combines downstrokes with upstrokes.
Write lyrics for the song. Punk songs are all about attitude. The lyrical content relies heavily on anger or teen angst, social and political commentary, and irony. One of the interesting things about the great punk bands is that they wrote short and catchy songs. In some cases, it the excessive volume and the punk clothing is removed, the songs could be taken for catchy pop songs.