Special moves are unlocked as you level up.
Sometimes the special move you receive will be an upgrade to an existing move to make it cooler. You can tell when moves have just been upgraded because they will be coloured differently. To perform a more impressive move, click and hold the move until it has finished cycling through the colours, then release and click on the floor to perform the move.
You can also perform some moves using the numbers on your keyboard!
Look out for special events that will make a special move available to players for a limited time only!