The day after the seventh day of Sukkot (also known as hoshana rabba) we have another Holiday: Shemini Atzeret which, technically, is a different holiday,independent from sukkot.
During Shemini Atzeret we do not have anymore the Mitzva of Lulab and Etrog.
As for the sukka, in Israel, during shemini atzeret the sukka should not be used. The meals should take place at home (lo tosif!). In the Diaspora, because of the ancient calendar system, we still use the sukka for the first day of Shemini Atzeret, but without reciting any blessing.
As any other holiday (Yom Tob), outside of Israel, Shemini Atzeret is celebrated during two days. The special thing about this Holiday's second day, known as Simchat Tora, is that it celebrates the end of the annual cycle of Tora reading and the uninterrupted beginning the new reading cycle, from bereshit.
We sing and dance around the Tora, expressing our joy for being part of the people chosen by God to follow His Tora.
Although, during the rest of the year we train ourselves to attain happiness independently of what we posses ("Success is getting what you want; happiness is wanting what you get") during Yom Tob, happiness should be given in addition a material expression. Yom Tob's happiness is expressed by wearing special clothing in honor of the Holiday (each one according to what he or she can afford) and by having a good meal (wine and meat, are a must in any Yom Tob's menu). It is also the obligation of the husband to ensure his wife's simcha of Yom Tob, buying her a new dress, jewelry, etc. (as for the husband's happiness, the rabbis explained, it is naturally ensured by seeing his wife's happiness. "Happy wife, happy life")
Chag Sameach!
Candle lighting in NYC: 5:51 PM