This was one of the reasons I thought I would never cruise. I get awful motion sickness, even in cars. When we first got on the boat, I thought I would just "see how it goes." But even docked at the port, simply going round and round the staircases, I was getting sick. So I took dramamine everyday and was fine. It was really amazing. I never felt anything.
For one of my daughters, who also gets sick in cars, I gave her dramamine as well. I didn't wait to see if the boat would affect her, because by the time symptoms show, it's already putting a damper on things. For the other daughter, who doesn't have problems traveling, we didn't give her anything and she was fine.
Remember that we are docked for most of the day at Nassau and Castaway, so you may not need it at those times. But when the ship is scheduled to be sailing, make sure you take something at least 20 minutes in advance of departure.