While it was originally used to describe country music, the phrase "three chords and the truth" is often used to describe many types of music, especially punk rock. If you're going to be the vocalist, you've got to provide the truth part. In general, punk lyrics need to come from your life, and come from the heart. Listen to Keith Morris' lyrics on the first two Circle Jerks records. He addresses class issues, politics, and addiction in explicit ways. Perfect punk vocals. Punk songs are often from the perspective of alienated youth, giving voice to the particular frustration of being a teenager. Feel like nobody cares or understands you? Channel that feeling into your lyrics. Sing about what matters to you, and to your community. Nihilism and anarchism are philosophies often associated with punk rock, both philosophies that privilege the freedom of the individual from all ideological and political structures. It's important to understand this context of most punk music. Most punk songs aren't incredibly complex in the vocal range required, or in the melodies included. Often, lots of classic punk lyrics will only include a few lines, repeated over and over. Don't worry about over complicating things. Often, punk lyrics don't need to rhyme to make them work. Toss out all the traditional rules of songwriting and go with what works for the material. Most punk songs are only two minutes long, three at the most. If you can clock in a memorable punk song that takes less than 120 seconds to play, you're really on to something. Don't overthink it when you're structuring the song. Think verse, chorus, verse, chorus, chorus. Punk rock also makes plenty of room for juvenile and the crude senses of humor. Toilet humor and sex puns are par for the course on lots of skate and pop punk songs, especially. Check out early NOFX, Blink 182, Screaming Weasels, and Green Day songs for good examples of punk at its most crude.

Summary:
Write the truth. Make the personal political. Write simple melodies. Make the songs short. Be crude.