I suffer horribly from seasickness. Surprisingly, that didn't keep me from working onboard the Disney Wonder but I still got sick all of the time. I basically lived off of Dramamine. I've found that the worst times to get sick, except for hurricane type weather, is when crossing the Gulf Stream about an hour or so after debarking and on the way back into port (on the East coast).
Though I've had to always use Dramamine, ginger is supposedly very helpful as well as stimulating acupressure points on your wrist. And the worst thing that you can do is sit there and think about it. I was once stuck in a cabin lying on the bed watching the closet curtains swing back and forth with the waves...this did not help the way I felt, needless to say. Try to get up and about as much as you can and don't watch the movement of the waves or the curtains. I used to have to lead dance parties when I just wanted to hurl myself over the side of the railing with seasickness and somehow the nausea always seemed to pass when I wasn't thinking about it.
At meal times, ask for a broth based soup, lots of crackers, and hot tea such as chamomile or peppermint to calm your stomach. Waiters are used to seasickness and can easily accommodate your request.