The most fully elaborated form is Chinese, and it is organised around the family line rather than around a deity.
The domestic altar holds spirit tablets inscribed with the names of the dead, often for several generations, together with an incense burner and offerings. Incense is lit daily or at intervals. Food is offered at festivals and on death anniversaries, cooked and served as it would be to the living and eaten by the family afterwards. Paper goods are burnt so that they transfer: paper money traditionally, and now paper houses, cars and telephones. At Qingming in spring the family goes to the grave, clears weeds, repairs the mound, offers food and burns paper. At the Hungry Ghost festival in the seventh lunar month offerings are made to the dead who have no descendants to feed them, and that festival is where the logic of the whole system becomes visible: a dead person without descendants is in serious trouble.
The obligation runs downward as well as upward. Failing to produce a son able to perform the rites was traditionally a grave matter, and the practice has accordingly shaped inheritance, adoption, marriage and household structure across East Asia for a very long time.
Japanese practice has a similar shape and different furniture: a butsudan, a Buddhist cabinet holding tablets and a memorial register, and Obon in summer, when the dead are guided home with lanterns and escorted back at the end of it. Korean chesa is more formal and more contested, because Korean Protestant churches have generally forbidden it, which splits families at precisely the moment the rite exists to unite them.
Sources Gods, Ghosts, and Ancestors: The Folk Religion of a Taiwanese VillageDavid K. Jordan with Ancestor Worship in Contemporary JapanRobert J. Smith, Ancestor Worship and Korean SocietyRoger L. Janelli and Dawnhee Yim Janelli