For all of the potentially queasy cruisers - I have one word for you:
BONINE!
It's an over the counter, chewable, daily, non-drowsy, motion sickness preventative.
Both DH and I are prone to motion sickness. We start taking this little miracle pill every morning about 5 days prior to the cruise. Keep taking it every morning on the cruise and take it for a few days afterward (until you get your sea legs back - you can actually be a little wobbly after you get off the ship - DH gets this more than I do).
It really, really helps.
The best solution to sea sickness is to never get sick in the first place. If you allow yourself to get sick, then you're fighting an uphill battle.
The first night out, as the ship cruises away from Florida, it is usually a little bumpy. Something about the currents that run parallel to the coast and the fact that the ship is traveling pretty quickly. If you're susceptible, you may also notice that you may feel the ship's motion in certain areas of the ship more than others. I find that I am more aware of that motion in the theater where the shows are and in Parrot Cay.
You'll be fine. If you feel yourself beginning to feel sick, make sure you get out on deck and get some fresh air. The wind on your face. It helps me to be able to see the horizon too - but that may not be the same for everyone.
Edited to add: I was posting at the same time as Brandie! Similar guidance from us both!