It depends on the activity. For the wall and the flow rider, you sign liability waivers and may have to wait a bit for your turn. I think they also have times set up for lessons, but I'm not sure about that. The virtual golf has reservations. Most things are first come - first served. The big issue is signing waivers for things where you could be injured - the wall, the surfing, ice skating.
All of this will be covered in the daily Cruise Compass, which is a schedule of activities for the ship. You get the Compass for the next day delivered to your cabin on the previous night - it is left on your bed when they prepare your cabin for the night time.
One thing that DOES require reservations is dining in the specialty restaurants. You really need to sign up for these on embarkation day. If you don't do it on the first day, you will probably not get a table.