The moon viewing held in mid-autumn is called tsukimi in Japan. It's a Japanese custom which originally came from China. Read about the Moon Festival in China.
Tsukimi is held on August 15th in the lunar calendar. It's called jugoya, which means the night of 15th. Jugoya in the solar calendar changes every year. It's usually in September or October. The moon on jugoya isn't always full, but it's said that the moon on the night is the brightest and the most beautiful in the year.
Tsukimi is done in a quiet manner in Japan. People look at the moon, enjoying the beauty. Tsukimi also has the meaning of celebrating the autumn harvest. Traditionally, susuki (pampas grass) or other autumn flowers are decorated in a vase, and dango (dumplings) and satoimo (taro potatoes) are offered to the moon in an alter. People often make dango at home. To make dango dumplings, rice flour is used. See how to make dango dumplings.
The word, tsukimi, is used in Japanese food as well. For example, tsukimi-soba and tsukimi-udon are well-known. They aren't food for moon viewing. Tsukimi indicates a cracked egg in Japanese cooking since the egg yolk resembles the moon. Tsukimi udon/soba are hot udon/soba noodle soup with raw egg toppings. McDonald's in Japan even sells tsukimi burgers, which are hamburgers with fried egg fillings.


