Because Japan is a country of volcanoes, there are more than 3,000 hot springs. Getting in a hot spring is one of the things you can enjoy after mountain climbing, and it soothes your fatigue as well. Japanese public baths, where you share a big bath with everyone, are places of soothing social exchange as well. Follow the rules, and relax and relieve your tired body.
Basically, there are showers in the washing space outside the bathtub. If not, put water from the bathtub in a washbasin and rinse your body.
Some facilities have a resting room to relax.
Although it's very unusual, there are some mixed baths in rustic hot-spring resorts in the Tohoku area. Some have separate entrances, but the bath inside is shared. However, even in such resorts, most facilities usually have separate bathtubs for men and women.