Sing from your guts. Punk is first and foremost about raw feelings. Anything else is a waste of time. No one will believe the punk singer who tweets on about theory or philosophy. Close your eyes, take a breath and let it rip.
Release your anger and let it be your guide. The foundations of punk lie largely in purposeful rage. Punk has always been about the common citizen expressing his dissatisfaction with the surrounding world. Not unlike the socially conscious lyrics of some rap music, punk often stands as the voice of the oppressed.
Use your body when singing. Punk rock requires no formal training, unlike opera, where lung capacity, pitch and posture play a large part. Where the opera singer's emotion is internal, a punk rock singer relies on releasing everything externally.
Listen to punk music. Listen to every single punk band possible. Copy a favorite singer, a group of singers or listen to what everyone else is doing, and then create something totally new. Also, watch bands perform live shows. This is the best source of inspiration around.
Practice with a band. This point is very important. Nobody ever became a great punk singer by sitting at home in front of the mirror. Find a drummer, a bassist and a guitar player and get to work (or just learn the guitar yourself and do both).