First, the birthday should be noted on your reservation. If this has not been done, call
DCL or your
travel agent. As above, they will confirm with you what night you wish to celebrate. There will be a cake and singing in the dining room. No candles are allowed as they are a fire risk. They sometimes have a "I'm celebrating" or "It's my birthday" button type pin. Concierge guests get a bigger celebration in their stateroom (at least sometimes). You are free to decorate your room or door for the birthday. If you purchase the birthday package the room will be decorated when you arrive, not on the birthday.
Nothing occurs in the Oceaneer's Club or Lab other than CM's wishing the child a happy birthday. They can't do parties and risk alienating the "non-birthday" kids. DD did take her leftover cake from the dining room to The Stack with she turned 13--as above, we didn't need another dessert, and were more than happy to share. You, of course, can take the leftover cake to the CMs in the Club and tell them that your DD wanted to share with them! This appears to be one time when they are allowed to break the rule about not eating guest food.