A good starting place is knowing what causes seasickness. It is now generally believed to be caused by a conflict between the eye (not seeing any motion) and the inner ear (sensing motion). If you are noticing any effects of the motion, the trick is to eliminate the conflict -- so be somewhere where you can see the horizon (and therefore the motion). Going up on deck is a great place, as you will get fresh air, which will help, and be able to see the motion. If you should need to go inside (to go to the bathroom, etc.), make it as brief as possible. Also, though it will seem counter-intuitive, eat normal meals. Stay away from greasy foods and don't overeat, but eat normally so that there is food in your stomach.
It has also been noted that the motion is not like a car or amusement park ride, and not like riding in a small boat either. A cruise ship does move in the seas, no ship is big enough to stop that, but the motion is a slower, more genteel motion. Cruise ships have stabilizers to minimize rolling motion (side-to-side), and ships endeavor to steer a course to minimize motion, but that is not always possible. Most passengers enjoy the motion.
There are some non-medical remedies/preventives. Clinical trials have proven the effectiveness of ginger in reducing motion sickness. You can take ginger pills (available in any drug store), eat candied ginger or ginger snaps or drink ginger ale, though you might have to drink a lot. This does not have to be started until just before the ship sails or even once you start getting ill, though you should take it in advance just in case.
Some people depend on sea bands, which apply accupressure to the wrist. These work for some people but not for everyone.
If you wish to take the medicine route, Bonine or Dramamine work for the vast majority of people. They are available over the counter. They should be started the morning the cruise starts.
If you have tried other remedies, and they have not worked, and you have an ongoing problem, a doctor might prescribe the patch -- a low-dose scopolamine treatment. These are not to be tried unless necessary, and have both some minor side effects, and the potential for serious side effects. If you know you need the patch, you should get a prescription a week or so in advance and try the patch on dry land. Most people just get a dry mouth, but there are some other serious side effects up to and including hallucinations.
Importantly, no do worry yourself into a problem. There is a mental component to seasickness, and some people essentially talk themselves into it. As I said, the vast majority of people have no problem whatsoever. Unless you really get motion sick, you likely will have to trouble on a cruise ship. If you should happen to, it will pass reasonably quickly, will be a manageable problem. Look forward to enjoying your cruise.
Oceania REGATTA - Scenic Panama Canal - Dec. 5 - Dec. 21, 2014
Uniworld RIVER AMBASSADOR - European Splendors, June, 2013
Disney DREAM - 4-Day Bahamas - January, 2013
Oceania RIVIERA - Accent on Italy - Oct. 24 - Nov. 3, 2012
MV ECLIPSE - 7 days in the Galapagos - June, 2012
HAL STATENDAM - 7 day Glacier excursion - June, 2010
Disney WONDER - 3-night Bahamas - Dec. 27-30, 2009
Oceania REGATTA - Scandinavian Splendors - Aug 8-22, 2009
Carnival FANTASY - 3-day 1990 or '91
USS HANCOCK (CVA-19) Two WestPac cruises 1969-71 Oops those weren't pleasure cruises!