You have to have a full power meter and you must perform a slash move or a special that has a slash for the final move.
Certain characters don't have the ability to kill people, Akari and Juzoh come to mind. I believe that Lee can't kill people either, but I'm not entirely certain on that one. I think one of the Faqs on the Gamefaqs site tells you who you can/can't kill people with.
One thing to note, if you play with Hibiki and kill everyone, you get a different ending than you do if leave anyone alive. Just a useless tidbit you may be interested in...