My daughter was 3 when we cruised last time. She had never been in daycare, or left with others than family. When we went on the cruise, all she wanted to do was go to the kids clubs and have mommy and daddy leave her alone. There were lots of different activities, and shows to see. We saw the show they took the kids too, but our daughter didn't want to sit with us, so she stayed with the kids, and mommy and daddy watched the show alone. We made her eat with us most of the time, but she desperately wanted to eat with the clubs (we did let her eat with them a few times).
Take a look at some of the navigators you can find on different sites. They list all the activities. Not just the kid ones, but the daily ones as well. What I did was go through the old ones and mark which ones interested me (and there are a lot of family ones). Then when onboard i knew which ones to look out for. I think the activities are usually at the same time, and day, for each type of cruise, but there is no guarentee. I felt it was easier to know what i would be interested in ahead of time, so i had an idea of what i was looking for if i didn't have a lot of time to plan out.