If you dance with your full suit on, you will produce fire with your flippers. When you wave, you will disappear (like the Cloud Wave Bracelets, but with fire). The Fire Amulet does not have to be worn with the suit.
To earn the Fire Suit, you must play against other penguins, many times, in Card-Jitsu Fire by being the last one standing, meaning you need to get your opponent(s) down to 0 energy. After you win a couple of times, Sensei will reward you with parts of the Fire Suit; first the Flame Sandals, then the Magma Coat, next the Lava Mask, and finally the Fiery Helmet. Then you can challenge Sensei in a battle, and become a Fire Ninja if you beat him and earn the Fire Gem on your Amulet.