This is a large topic, and some background information will really help you before we get to remedies.
First of all, most people don't get seasick, and if you do, it almost always passes in a day, once you get your sea legs. Yes, I know, there are some people (a very small number) who seem to take several days to get over it.
Seasickness is primarily caused by a conflict between the eyes (if they are not seeing the motion) and the inner ear which detect the motion. So, prevention is somewhat easy -- stay someplace where you can see the motion until you get your sea legs. Staying out on deck and watching the horizon is the cure, and the fresh air will help as well. If you are inside, stay near a window so you can see the horizon. If you are not feeling well, do not go inside and lose sight of the seas. The other thing is to eat normally. While this seems counter-intuitive, an empty stomach is not the answer. Keep away from greasy foods and don't overeat, but eat normal meals at normal times.
As for the remedies:
Ginger is clinically proven to dramatically reduce or prevent all motion sickness. You can take ginger pills (available in any drug store), eat candied ginger or ginger snaps, or drink real ginger ale (though you might need a lot). This is a natural remedy obviously, but clinically proven to work. It is also used to reduce nausea on land and often with chemo therapy, so it might (I have absolutely no idea) help with your morning sickness. Who knows? Start taking or eating it before you get on the ship, but you do not need more than a few hours' time for it to get into your system.
Some people, as noted in a previous post, swear by the seabands, others notice no effect whatsoever. Again, no medications, but not always effective.
Bonine and dramamine are OTC medications available everywhere. They will work for most people who get seasick. They should be started before getting on the ship. Ships also dispense generic forms of these pills. Here, however, check with your doctor before taking any OTC medications.
This is where I would normally mention the patch, but there is no way I would even get into it if you are pregnant. The patch contains scopolamine with is a very, very strong drug. Even with people who are not pregnant, it is really for people who have tried everything else, and nothing works. I'm no doctor, but I would stay away from this.
Perhaps most of all, don't worry yourself into it. If you don't get motion sick in other situations, you are likely to be fine or will be fine after a few hours. While cruise ships do move in the seas, and rough seas can cause a lot of motion, bear in mind that they are not anything like small pleasure craft that bob and bounce along all the time. Motion on a cruise ship tends to be much, much slower and less dramatic. If it were a really common problem, you wouldn't see so many cruise ships out there. For most passengers, the gentle motion is calming. Cruise lines try to avoid rough seas when they can, though that is not always possible, and the seas are not always coming from the right direction (Mother Nature can be soooo finicky). For the most part, though, relax and enjoy. Odds are that you are going to be just fine, and the initial prevention suggestions should be enough by themselves.