How to Avoid Seasickness
1. First and most common way: pills. Over-the-counter anti-emetic drugs like Dramamine, Bonine, or Marezine are small, chewable tablets that are readily available in any drugstore or grocery store pharmacy. Take one every 12 to 24 hours (read the package instructions), with the first one an hour before the boat leaves the dock. If the boating activity is on a cruise ship or otherwise hosted expedition, the boat might carry a supply of meclizine (generic of Bonine).
2. Then there's scopalamine patches. These are small, round, typically skin colored (for light-colored skin), and placed behind the ear. One patch is good for three days. They are expensive, however, and available only by prescription. Don't use more than one at a time.
3. Acupressure wristbands like Sea Band. There is a pressure point on the inside of each wrist which, when pressed hard enough, will silence the nerves that cause nausea. Finding the right spot can be tricky, however, and the spots on both wrists must be firmly pressed for it to work. Acupressure wristbands come with very tight elastic and a small button to do the pressing. The elastic is good for several years before it wears out and the wristbands lose effectiveness.
4. Motion Eaze is a liquid made of "natural oils." Like the scopalamine patch, it is absorbed through the skin.
5. Ginger (in the form of ginger gum in the picture above) may be effective on very mild cases of seasickness. The very first part of seasickness is increased sleepiness, and ginger will stimulate alertness.
How to Ease Seasickness In Progress
If your prevention methods have failed and you feel sick, don't hide inside or below-deck - that will just make it worse. You need to be able to see the horizon, which means you need to be outside. Sit on as low a level of the boat as possible, and as close to the middle as you can get while still being outside. Tall boats sway more up top than at the water surface, and rock more at their sides. You're looking for the part with the least motion.
Also, try to avoid places with too much engine noise or fuel fumes. If you can't see the horizon (it's dark or foggy), focus on anything you can see that's as far away as possible - wave crests (not the swirly ones right by the boat!), the moon or stars, clouds, etc.
Preparing to Vomit
If you know you will be vomiting, there are a number of things to do in advance. First, figure out which way is downwind (probably facing to the back of the boat) and where on the deck has the least wind. Check that there are no people immediately downwind of your chosen spot. You do not want to vomit while facing the wind, as it will come right back and land on your face. It's also considered bad form for it to land on other people.
If it's a small boat on calm waters, leaning over the side is the preferred way to go. On larger ships in the open seas, be sure to wear a life jacket. However, leaning over the side isn't strictly necessary if the boat comes equipped with deck-cleaning hoses that you can access. All outside decks are waterproof, and if you have access to a hose, you can simply rinse off afterward.
Make sure you have lots of paper towels and kleenex stashed away in your pockets, so you can clean yourself up afterward as well. Kleenex is important if any of the vomit goes through your nose.
What to do After Vomiting
Afterward, eat starchy foods like rice, potatoes, bread, or crackers. Those will help settle your stomach. Eat something even if you aren't hungry. If nothing else, it gives your stomach something to empty if you need to vomit again later - which, while uncomfortable, is still better than vomiting nothing.
Landsickness
The good news is that eventually, if your boating trip lasts long enough, you will probably develop your "sea legs." The balance centers of your brain will adapt to the rocking motion and you'll stop noticing it.
The bad news is that you might go through the reverse process once you're back on land. This is called either "dock rock" or "landsickness" depending on how long it lasts. Basically it feels like perfectly still ground is moving, and your body will sway to try to counter the rocking motion that isn't happening - sometimes to the point where you lose your balance. Depending on how long your trip was, it can take up to a week to go away.