Here's how it worked. You fill it up with cold water, turn on the gas, turn on the water heater, and the water heater starts to circulate the water through itself to warm it up. You then stand on the wooden platform, get out your buckets (below) and start scooping water over yourself. Do your thing with the soap, shampoo, etc. and then return to dumping more water until you feel rinsed. Repeat as desired.
Then, and only then, it is time for a nice soak in the water. There is nothing better than soaking in a tub so deep the water comes up to your chin. And it is so much fun to splash around and throw water on the floor (probably only because I was an American kid with an American tub who got into trouble for doing that).
The novelty of this whole thing does start to wear off by about November, though. The apartment doesn't have central heating, and electric heaters around water are not a good thing. So you are standing there naked and soaking wet in a freezing cold bathroom, frantically scrubbing and dumping water over your head. My thought was that since I am not Japanese, I could just wash in the tub instead, but then if I got into the tub all soapy, the only option would be to rinse with cold water. The good news is that it really does make you appreciate a good long soak that will keep you warm for hours to come.