This advice was for an exchange student going on a brief
homestay during summer.
I have very little information about using an onsen for guys, though, from what I hear, it's fairly similar.
1. When bathing, you bathe outside of the tub and soak in the tub, or ofuro, afterwards.
2. *Don't let soap or suds get into the ofuro water.* Everyone in the house uses the same ofuro; so you have to keep the water clean. Sometimes this is hard when you have a shower next to the ofuro. If you do get any soap in the water, scoop it out quickly with a basin.
3. Don't let your hair get into the ofuro water.
4. Most private ofuro have some sort of shower in them, usually a hose with a shower head attached directly to the ofuro faucet. But there are many different designs of ofuro and faucets; if you are unsure what to do or how something works, ask. Usually your homestay will show you.
5. The typical bathing senerio is to sit on a low, plastic or wooden stool and dump basins of water over yourself to wash and rinse. With a large ofuro, like what you'd find at a hot spring, or onsen, many people will use ofuro water to do this. But you have to be careful to keep the basin from getting soap on it, if you do.
6. If you travel and do not stay in a western style hotel, you will likely end up in a public or semi-public bathing situation. If you are shy about this, cope. The vast majority of public ofuro are separate sex, so at least you won't have to worry about that. ^_^
7. If you are bathing in a public ofuro, *do not* stand up to shower.
8. Some people will stare at gaijin in an ofuro, but most women won't. I think, perhaps, if you're aclimated to Japan enough to use an ofuro, then you aren't considered -too- foriegn. Besides, staring is rude. ^^ I have never had a negative ofuro experience and I've been all over Japan. Actually, I have many fond memories of 'onsenning'.
9. In some public ofuro, people use small towels to cover their privates. I haven't actually seen this in person, but this is another watch and imitate situation.
10. If you go to a hotel with an onsen, or hot spring, you will find various things in your room for you to use, including geta (wooden clogs), a yukata (light, summer kimono) and a tenzen (heavy, outter kimono). You are expected to wear these things to and from the onsen. Please, remember when using yukata and kimono, the left side goes over, the right side under. The other way around is only for the dead. ^^' Among the things you'll find in your room, you should also have one of the little towels mentioned in 9. You can keep it. Most have the onsen's logo on it; I find they make great keepsakes.