Ah, hot springs. One of the finer parts of life in Japan. You should definitely experience one while you're there. While there can also be some very real experiences in culture shock while you're there, the onsen is absolutely worth adapting to the local culture.
Nudity: May as well get this one out of the way. Yeah, the overwhelming majority of hot springs involve nudity. This is why they're sex-segregated. There are non-nude places where co-ed groups of friends can go together. Still, nudity is the rule rather than the exception and for the most part you'll end up with old people who don't bother you.
Cover up tattoos: At most hot springs, tattoos are banned for their Japanese cultural connections to yakuza mobsters. You're almost certainly not a mobster yourself, but rules are rules. Welcome to Japanese culture. If you have small tattoos, use gauze and medical tape to cover them up and you'll be fine. If you have a giant sprawling tattoo, you may as well stop reading now. Your mileage will vary, but generally a heavily tattooed person will have significant issues with getting let into most hot springs.
Pay up front for what you need: Some places (especially those in the cities) will have vending machines in the front that you'll pay for your entrance ticket. If the machines also offer towels, shampoo or soap, you should pay up now or bring your own. Plenty of places will offer those for free, though.
Bathe thoroughly! You should be 100% squeaky clean before actually getting in the hot water. In the picture above you can see little stools and faucets. Those are for use bathing yourself. Plenty of places will have shampoo and soap bottles right there, but if not this is where you'll need the stuff you bought or brought along. DO NOT let soapsuds get into the hot springs!
Use a little washcloth for modesty: Just cover up your most sensitive parts with it. Once you're in the water, feel free to set the washcloth to the side or drape it over your head to warm up.
Alternate between hot and cold baths: If your hot springs has a cold bath, give it a shot! Normally people switch between the two, a few minutes at a time. Tradition dictates ending on the cold one.
If old people bother you about your looks: While it's rare, you may occasionally be harassed by otherwise harmless little old Japanese people about your exotic foreign looks. While experienced expats just gracefully let it roll off their shoulders, feel free to leave if you're uncomfortable.
Go when it's cold! It's a fantastically refreshing sensation. That goes double for outdoor hot springs.
Photo credit: AliveNotDead
For native Japanese, one of the most popular forms of tourism is to travel to a hot springs resort. They come in all varieties, from remote and romantic to convenient and family-friendly.
They'll provide you with a yukata for lounging around and sleeping and many have an option for meals. The quality of the meals will scale with the price you pay, but native Japanese know that high-end hot springs resorts often serve some of the best meals in the country.
Because it's such a common form of travel, transportation is pretty well-established to almost all the major resorts. Trains will get you close to the ones relatively near major cities or train lines, and plentiful buses will get you to the more remote areas.
If you want to reserve a night at a Japanese hot springs for your trip, just click that little banner for a website in English that'll help you out.