There are a variety of customs in connection with the degree to which the Sukkah is "lived in" on Shmini Atzeret. One custom is to eat both the evening meal and the following day's meal in the Sukkah, as on Sukkot. A second custom is to eat at night but only make Kiddush during the day, still another just to make Kiddush at night (and any other permutation and combination, perhaps, as well), because the Mitzvah of Sukkah has really terminated with the end of the seventh day. The various customs arise from the idea of not to "just run out" of the beautiful and meaningful Sukkah. All of the above customs agree that the blessing "Layshev BaSukkah," "To dwell in the Sukkah" is not said on Shmini Atzeret , again because the Mitzvah is really over.
There is a widely, if not universally, accepted custom to eat cake or fruit, and have a drink (alcoholic or non-alcoholic) in the Sukkah on the afternoon of Shmini Atzeret. After this is done, usually in a party-like setting, we say goodbye to the Sukkah for the current year by reciting the following prayer:
"May it be Your will, Hashem, our G-d and the G-d of our forefathers, that just as I have fulfilled the mitzvah and dwelled in this Sukkah, so may I merit in the coming year to dwell in the Sukkah of the skin of the Leviathan(2)."