The word onsen is often translated as hot springs, but the truth is we really don't have anything that actually equates. Onsen is not just hot water coming out of the ground, it's a unique cultural ritual found only in Japan. It's also a place where traditionally the social hierarchy is ignored and everyone is equal.
It is still Japan, however, so there is a rigid protocol for how to bathe properly. I'll do my best to lay it out here:
First, you have to get totally naked. If you wear a swimsuit everyone will assume that you are either hiding something or that you are dirty down there. If you wear one you might get kicked out, but I don't really know because I've never actually seen anyone try it. Just relax. Everyone else is going to be naked too and it's no big deal here. They show men in the onsen on TV all the time.
And guys, don't be weirded out if there are female attendants in the men's changing room. In Japan it's OK for women to see men naked (but not vice versa, so don't worry ladies).
Next, proceed to the bank of showers, sit down on a plastic stool, and thoroughly wash yourself. You have to wash yourself where everyone can see you. This way everyone knows that everyone else is clean before they get into the shared baths, because the onsen water is totally natural and unchlorinated. Don't bother showering before you go, because you will have to shower again once you're there.
Now you're free to relax and soak. There's technically a procedure about which baths to get into in which order and how to properly immerse yourself, but I usually just do whatever I feel like at this point. Depending on the place, there are a lot of different kinds of tubs and saunas and steam rooms and stuff like that. There are also indoor and outdoor tubs (with privacy walls to keep out the peepers). My advice is to try them all.
Finally, when you are done, don't rinse off. The onsen water is loaded with all sorts of minerals and things that are therapeutic and beneficial and all that. Kusastsu onsen--a particularly famous onsen that we just happened to visit today--is reputed to cure all ailments except love sickness. They have manga porn to help you deal with that.
Yubatake: the source of Kusatsu onsen. It stinks like rotten eggs.