This advice was for an exchange student going on a brief homestay during summer.
1. It rains a lot, especially in summer; take a lightweight, waterproof rain jacket, preferably stowable, with a hood.
2. People usually leave their umbrellas in stands, outside, when they come into a building, some places even have locks and keys for them. Because these things are designed for long umbrellas (collapsible are uncommon) you might want to buy a long umbrella there instead of bringing your own. Your homestay may provide one for you.
3. When it's raining and you enter a department store with an umbrella, there are strips of plastic and trashcans in the entrance. These strips are bags you put around your umbrella so that you don't leak on the floor. Be sure not to poke a hole in the bottom!
4. Which leads us to a general rule: When in Rome... If you aren't sure what to do, watch to see what other people do and imitate them.
5. Most public toilets are not western and ones in train stations and such usually have no toilet paper. Carry tissue with you (your homestay will probably have some if you forget), and, when using a non-Western toilet, face the raised rim and don't sit on it. I have a theory that these toilets are the #1 reason most women in Japan wear skirts more than we do.
6. If you end up someplace with a fancy toilet, *DON'T
PRESS THE BUTTONS!!!* Go to the bathroom, lower the lid and seek assistance.
>I have absolutely no idea...Japanese toilets are starting to sound really scary...
>> The Japanese toilets aren't scary, once you get used to squatting. It's the fancy, high-tech Western ones which are scary; you can't be sure which button might be the bidet. O_O
7. If, for some odd reason, you end up using up a roll of toilet paper and have to replace the roll, make sure that the loose part comes over the top, not out the bottom. In Japan, this is universal, believe it or not.
8. Men's rooms in train stations sometimes have no doors; so don't look in.
9. Some men in Japan will pee anywhere. If you see a man outside, facing close to a wall or pole or hedge, he might be relieving himself. You can deal with this as you see fit (laugh, be embarrassed, ignore it, whatever) just be aware that it happens. (Old men can't always control themselves long enough to make it to a bathroom and construction workers sometimes don't have toilet facilities... some people are just gross)
10. If you're going to have your period, I recommend bringing your own feminine supplies. Besides that it's just more comfortable to have your own, Japanese versions of similar products are sometimes not what you expect. That, and if you buy any, they often package it an a special pink or floral bag as though to announce to the world "SHE'S HAVING HER PERIOD!!!" -_-'