If you haven't been to other countries before, it may be a little interesting to know that bathrooms everywhere in the world are NOT the same. Although Taiwan is influenced by Western culture, there is actually an interesting blend of East and West here.
In the home, if you have a host family, you can expect to have a Western toilet, as in the ones that have a lid and seat, you can sit on them, the "average" toilet. However, in schools and many other public bathrooms, you will have the scary squat toilets that are nothing more than a ceramic-lined hole in the ground. If you have never used one before you might wonder how you use it, but it's simple, squat. The restrooms in hotels, malls, and bus stations will most likely have Western toilets, however.
It is something to note that in any bathroom besides the one in your house, you must bring your own toilet paper! Tissues are used for everything here in Taiwan, so don't bring a roll of toilet paper, just bring a pack of tissues everywhere with you. Once again some of the bathrooms, like in the bus station, will provide toilet paper, but don't rely on that. Schools will not provide it for you.
Additionally, you may see signs telling you not to flush the toilet paper in the toilet, but to dispose of it in the trashcan nearby. This is to prevent clogging, so just try your best not to clog their toilets!
As for soap, I have seen probably one or two bathrooms this entire time that provided soap. It's a little disgusting to me, but most people just rinse off their hands and leave (let's be honest though, so many people do that in the USA when they think nobody else is in the bathroom). Even at my house I had to put out soap to use! If you like being clean, bring some hand sanitizers with you, because those aren't common here either.