Many Western people are not used to sitting on the floor. In Japan, however, sitting upright on the floor is common in various situations. For example, meals are traditionally held sitting on the tatami floor around a low table. Also during the tea ceremony and other traditional events, one sits on the floor.
The formal way of sitting for both genders is kneeling (seiza). People who are not used to sitting in seiza style, may feel uncomfortable after a few minutes, and their legs may get numb. However, foreigners are not usually expected to be able to sit in seiza style for a long time, and an increasing number of Japanese people themselves aren't able to do so due to a westernized lifestyle.
In casual situations, men usually sit cross-legged, while women sit on their knees laying both legs to one side. The former sitting style is considered exclusively male, while the latter is considered exclusively female.
The most important guest sits on the honored seat (kamiza) which is located farthest from the entrance. If there is a tokonoma in the room, the guest should be seated in front of it. The host or least important person is supposed to sit next to the entrance (shimoza). Of course, there are more factors to be considered in every specific case.
A lot of Japanese households consist of one or more traditional Japanese style rooms with tatami floors as well as modern rooms that usually have wooden floors. Tatami mats are made of straw and measure roughly 180 cm x 90 cm. You should always take off your slippers when stepping on tatami mats in order to protect them from damage.
Traditional Japanese style tatami rooms have an alcove (tokonoma) in which a hanging scroll (kakejiku) and a flower arrangement (ikebana) or piece of pottery is displayed. The room entrances are sliding paper doors (fusuma) and sliding paper screens (shoji) which can be removed completely.