Confession: I am a cruise ship writer who gets seasick.
First of all, big modern ships with stabilizers do not have the same level of choppiness as, say, riding in your pal's fishing boat. You are more likely to experience smooth seas than not, especially if you stick to calmer water routes such as the Caribbean in winter or Alaska's Inside Passage.
Make sure to keep your belly full (an easy task on cruise ships). Even though its sounds counterintuitive, having a full stomach eases seasickness.
If you do feel movement, and it starts to make you queasy, take a pill. My go-to when things get bad is a half of a Bonine, more if needed. Some people swear by homeopathic remedies such as acupressure wristbands and ginger pills. They don't work for me, personally, but might be worth a try.
If I'm spending many consecutive days at sea, I bring along Transderm Scop patches that you place behind your ear for continuous medication. But the truth is I rarely need them; they are more of a security blanket. Through my experience, I've learned that if the seas reach my tolerance limit, I'll feel less queasy if I just lie down.
Having taken more than 150 cruises, I've been truly sick only twice -- both times on small ships, where you are more likely to feel motion. My advice is to test your own sea legs by doing a short three- or four-day sailing on a big ship, first. Or try a river cruise, where you're likely to feel less movement than you would in a car.
Bottom line: Between more stable ships and trusted remedies, there’s no need reason to let fear of seasickness keep you from cruising.