A special move is activated with B after collecting 5 stars. You will need to perform a special move with the 6 starting characters as well as the 6 locked characters. Here is how you unlock them:
Toothless - complete wind cup 50cc
Marty - complete moon cup 50cc
Fiona - complete one challenge
Alternate Shrek - complete all circuits in 100cc
Alternate Skipper - complete all circuits in 150cc
Alternate Alex - complete all mirror circuits
While the 3 alternate characters have the same specials as their normal counterpart, you will still need to perform a special attack with them.