In the Club and Lab, you don't really make reservations. Every child on board the ship has a reserved place in the programming. You do need to register to indicate that they will be participating (this doesn't obligate you to a time or anything, just says that they can come). You indicate any allergies, special needs, etc. and give your cabin number and who is authorized to pick up your child (or that an older child can sign himself in or out.)
Currently, you can register on line if you have paid in full for your cruise, you can register at the terminal, or you can register after you board the ship. There is no real advantage to on-line except that it will save you a little time after boarding. You will still need to go to the club or lab to get your ID tag and beeper.
Then, when the child wants to participate, you take them to the appropriate place and sign them in. It takes about 30 seconds to sign in since they are already registered.