In my experience (a total of over 4 months at sea, about half of which was in the Southern Ocean) most people get over seasickness after a day or two. Some people are really unlucky and will still get sick as soon as the sea isn't totally flat, there's no way of telling in advance which you are. So stocking up with appropriate drugs is a good idea.
Bigger ships are usually more stable and the closer to the middle (both bow-stern and up-down) you are the less movement there is. Ships with the accommodation over the bows are pretty much the worst for seasickness, but those don't tend to be used for cruises. A lot of people find that being able to see the horizon helps a lot. Avoid computer games, reading and watching movies.
If it's rough enough then almost everyone will get sick, even the crew. I found the best thing to do then was just stay in my bunk, being upright made the nausea worse and if it's that rough then your bunk is the safest place to be.