The thing about any seasickness advice is that it's all dependent on the individual. Some people get it, some don't. It changes throughout your life. Some people respond well to some drugs, some don't. And so on. I think the best thing to do is, if you're worried about it, talk to your doctor before hand, and then bring anything you might want to try -- ginger, prescriptions, over the counter meds, sea bands -- with you on the cruise. Yes, they sell some of them in the shops, but in some cases for a LOT more (says the woman who spent a small fortune on Dramamine last cruise).
I definitely second talking to your doctor and bringing what you think you will need with you.
For example, the generic meclizine that is available for free on the ship, at least when we previously cruised with Disney, may include an ingredient you cannot have. In my case, the chewable tablets contained aspartame, which I get a severe adverse reaction to.
I get motion sickness on ships and boats and sometimes in land vehicles and on certain rides (no spinning teacups for me).
My personal solution for cruising, refined on our last cruise:
I am not willing to try the patch because after reading the potential side effects (both common and the less common) *I* was not willing to use it. Plus, I get bad rashes from adhesives and had no desire to spend the cruise and some time after with an unhappy rash. My sister does use it. Talk with your doctor and make your own choice if it is an option.
I wear
SeaBands, 24/7 except for showering, from the day before the cruise until a few days after we get off the ship. I use the original brand name ones, as they have been clinically tested to be effective. I do note that wearing them all the time the skin beneath the "ball" can get a bit irritated. I found that if it is too bad taking the band off briefly and massaging the area can help, but I have not yet found a long-term solution to that issue. usually I find the time I take them off for a shower coupled with massaging the area during that time is mostly sufficient. Note that when they are off the motion sickness symptoms may be stronger.
I take
Dramamine Less Drowsy (active ingredient: Meclizine HCI 25mg; see info at
http://www.dramamine.com/motion-sickness-medicine/less-drowsy/ ). I take one tablet each night starting the night before we board the ship and ending a few days after we get off the ship (I also have motion issues once we are back on land). I can add a second tablet if needed. Since I am Canadian, you cannot buy this (or any meclizine) in Canada, but I pick it up when I visit the US, where it is OTC in many stores; just check the expiry dates on the containers. I have found that by taking it at night the worst of its side effects (for me potentially some sleepiness) happen when I am sleeping; I have previously taken it in the morning and at home for other reasons have taken it in the daytime and find I notice the side effects more when I do.
I take
Dramamine® Non-Drowsy Naturals (active ingredient: Ginger,1000mg; see info at
http://www.dramamine.com/motion-sickness-medicine/non-drowsy-naturals/ ). I take one capsule each morning and each night. It is easily increased if that is not enough to the maximum indicated on the label. In Canada, Gravol has two equivalents - gel cap or tablet, with slightly different doses:
http://gravol.ca/en/products/natural-source/gravol-®-natural-source-ginger-liquid-gel-capsules/?cat=5 and
http://gravol.ca/en/products/natural-source/gravol®-natural-source®-ginger-tablets-ages-6/?cat=5 they also have lozenges but there is an ingredient in them I cannot have; Gravol has a webpage with more info about ginger in general and their products specifically:
http://gravol.ca/en/resources/about-ginger/ ).
I had initially looked at other ginger products, such as ginger candies and such, but ran into a couple problems: (1) there is no dosage control, so you don't actually know how much ginger you are getting; and (2) I have numerous food allergies and could not find any that were safe (one company I wrote to was really great, explaining their product would not be safe for me and why, but referring me to a competitor's product they thought MIGHT be; alas it also was not safe). I usse the dramamine/gravol ginger products at home for other types of nausea so am comfortable using them and know they help.
I bring
Ginger snap cookies that have proven their worth at home. I prefer Shasha brand ginger snaps (
http://www.shashabread.com/products/original-ginger-snaps and can be ordered through many retailors including
Amazon) which I find work well, are readily portable, and are allergy-safe for me (they are made in a nut-free and dairy-free facility). Our first two cruises I ate a lot of them; this last cruise I did not even open the two bags I brought... Next cruise I think I will just bring one bag.
I bring
Ginger Ale bottles. My preferred brand is Canada Dry and there are some brands I really do not like the taste of. We brought 6 bottles this time and we pack them in our carry-on to bring them on board. I did not need to use all 6.
Ginger Ale is also available for free in the MDRs at all meals. There is nothing wrong with drinking ginger ale for breakfast

(and FYI, it mixes nicely with cranberry juice if you want to convince yourself you are not drinking ginger ale for breakfast).
I have
"normal" Dramamine/Gravol as a backup in case it is needed because the above do not work well enough. It DOES make me drowsy, so I reserve it for when the alternative is less desirable than possibly having to take a nap. I also have
Benadryl on hand as a less effective (than normal Gravol/Dramamine) but also less drowsy-making (for me) backup. If possible I reserve those for nighttime when sleeping won't matter and it is also IME usually when the ship motion is often worst.
Sleeping position: one night on our second cruise the seas were rather rough. I accidentally found that if I lay perpendicular in the bed (i.e. head at one side of the bed, feet at the other, as opposed to the normal head at the head feet at the foot) that the motion was less severe. I slept that way that night and it seemed to help. So, experimenting with sleeping position might be helpful (or e.g. switching to sleeping on the couch bed, which is usually perpendicular to the main bed).
YMMV. Speak with your doctor and pharmacist -- they know your situation best and can provide tailored-to-you professional advice.
SW