You don't see traditional Japanese footwear very often these days, as it is usually only worn with other traditional clothing. Geta shoes are raised wooden shoes worn with the informal yukata.
Geta are most often seen on the feet of sumo wrestlers these days. You will most likely hear them before you see them, as they make a distinctive clattering sound when the wearer walks. This is sometimes mentioned as one of the sounds that older Japanese people miss most in modern life.
As in many other aspects of life, the fashion of the early Japanese nobility was heavily influenced by Chinese culture and so they wore shoes or boots.
The origins of the geta lie in the Heian period (794-1192), a time when a more "native" culture developed.
Geta are made from a flat piece of wood on two lasts (called ha or teeth) that raise the sole part 4-5 cm off the ground.
This is enough to protect a kimono from dirt, although ashida (rain shoes) have slats about 10 cm high. Some sushi chefs even wear geta with ha that are up to 17cm high.
These "platform shoes" were revived in a brief fashion trend in the late 90s, when young girls were seen tottering around on atsuzoku (thick heels).
While geta have become quite rare, the shoe cupboard in the genkan (entrance hallway) of every house is still called a getabako (geta box).
When you enter the genkan, you have to take off your shoes and the formal etiquette is to leave them neatly aligned and to the side, facing inwards.
The host turns them around and places them in the middle before you leave. Younger people tend not to care about these niceties.
But when entering shrine or temple buildings and many Japanese-style restaurants, you are expected to remove your shoes.
Many restaurants and houses provide slippers for their guests, but they should be removed when entering a room with a tatami mat floor. There is also a separate pair of slippers that must be put on in the toilet.
Geta designs vary greatly depending on their use. Pokkuri geta are for young girls and have indented bottoms that make a nice sound when used; koshi geta are used in the rain; yuki geta are designed not to catch or hold snow; niwa geta are for use in the garden; nori geta are used by seaweed harvesters in water.