When taking a shower or bath in Japan, the most important thing to know is that you must be absolutely clean before entering the bathtub. To do that, you have to take a shower outside the tub (the floor with the diagonal lines in this picture). Be careful not to get stray soap or hair in the tub, since the full bathtub will be used by everyone in the family.
The second most important thing is that everyone bathes at night, usually between 7-10pm. Please respect this custom at your homestay; your host family will love you for it!
Some useful words...
A- the bathtub, or ohuro
B- a shower stool, or shawaa isu
C- a plastic basin, or senmenki
D- a lever, or rebaa
E- the faucet, or jaguchi
F- the shower head, or shawaa heddo
*Your host family may or may not have a shower stool and basin in the bathroom. Some families will have a thick, soft, plastic mat on the floor instead.
*If your homestay bathroom has a lever next to the faucet, point the shower head away from you while you try the tap, unless you would like to be surprised by a burst of cold water from an unexpected direction. :)
*I have yet to see a shower head stuck to the wall in Japan. They are all detachable for convenience.
*Japanese hotels often provide body soap, shampoo, and rinse (conditioner).
Japanese bathrooms are usually in their own area of the house, next to the toilet room, sink, and washing machine. This forms a sort of hall that can be closed off with a sliding door, so when you take a shower, just close the door and leave your towel and clothes outside the bathroom. When you finish, grab the towel and dry off inside the bathroom so as not to create a puddle on the floor outside.
Some homes have an electronic pad on the wall of the bathroom. Ask your host family to explain it to you; it's for turning on the hot water, but there are other buttons, such as a "panic button" that will send your confused mutters straight to the kitchen.