The O.Club isn't like Flounder's Nursery or the Spa or Palo's where there are a limited number of spots so you need to run to sign up. My understanding is that if you have a child in that age range, he/she is eligible for the club. It is convenient to sign him/her up the first day so you can meet all of the counselors and such, but you can sign up later if you prefer.
The only thing I have heard is that on weeks where there are an abnormally high number of children, they sometimes run out of beepers (which they issue to each family for the duration of your cruise so you can be contacted if needed). Hasn't happened to us, but I have read about it in other's posts.
On the first day of the cruise, just go to the Club and the counselors are there to meet you and the child, fill out a brief form about the child, issue you a beeper, and show you around the club. When/how often you use the club is up to you. You don't need to "register" for times, just drop and go! The only restriction is that when the groups are "in transit" (like going to and from lunch) you are not able to drop off or pick up your child.
HTH!