I've done some experimenting on bots, and just the act of hurting someone will increase your powerlevel. I've also been told that being killed by someone with a powerlevel higher than yours will increase it, but I'm not sure if that's true or not.
To transform, your powerlevel has to be high enough. (It'll tell you how high it has to be in the description of the character on the character selection screen.) When you're at the requisite powerlevel, just push z.