Etiquette

Onsen means hot springs in Japanese. They are public baths (we could find private bath in some resorts) where men and women are separated so before entering in, it is important to pay attention to the color of the "noren" curtains which are generally blue for men (with the character 男 wrote on it :man in Japanese) and red for women (with the character 女). Sometimes, there are some resorts which switch baths so the bath that is for men in the evening may be for women the next morning.

In the bath, you will have to be nude and you will have to take a shower before entering in. Typically, you will find showers just next to the bath with toiletries provided (shampoo, soap...) and a small tool. It could have rustics onsen where toiletries and showers are not provided and if so, you will find a wooden bucket next to the bath with which you could rinse yourself before. It is possible to take a little towel with you but it is strictly prohibited to put it in the water so you could move it to the top of your head. 

Tattoos are usually not allowed in some onsen but you could buy bandages in Konbini in order to cover them. (You should notice that it could be some resorts that not allowed even the covered tattoos)

In Japan, there is a large number of Buddhist temples, Shinto shrines and sanctuaries and it is important to respect some rules while you are visiting :
 
Water purification, Temizuya or Chozuya

At the beginning of the visit of a Shinto Shrine or sanctuary, you will find yourself in front of a little water spring where you will find "Hishaku", Japanese wooden ladles with which you will have to rinse your hands (usually the left hand before) in order to purify before praying to the gods.(Shinto is an ancestral religion that honor many gods and deities). 

The entrance to the temple 

When you enter a temple, you should bow in front of the Torii (traditional Japanese gate usually red because this color casts out bad spirits) before passing under. After that, you can freely stroll into the sanctuary. 

How to pray 

You will find a rope called "Shimenawa" and an offertory box  where you will have to throw a coin (typically a five-yen coin). 
The manners are to bow once you get to the front of the shrine, to throw a coin into the offertory box; to move the Shimenagawa and bow twice; to clap your hands twice and bow once more. It could be different manners of praying regarding the sanctuary you are visiting but this manner is commonly used.
Please make sure that taking pictures is allowed before doing; and notice that some temples required you to take off your shoes before entering.

Ema and Omikuji

In most of the temples, you could buy "Ema" that are little plaques which on you could write your wishes and then hang it up on the shrine grounds.
It also exists "Omikuji" which are random fortunes written on pieces of paper that you randomly choose from a wooden box near the sanctuary. It could be bad or good fortune and if it is a good fortune, carefully carry the paper with you. In the other case, do not worry, you will have the chance to hang it to a tree in the sanctuary and the Shinto priests will take it and burn it in order to make the bad fortune disappear.