Simchat Torah and Shemini Atzeret are one day. Outside the Land of Israel, however, where all Festivals are observed for two days, they are separate. The first day is reserved for the joy of the Festival and for the prayers for rain, while the second day is reserved for the celebration of the conclusion of the cycle of reading from the Torah. (Some communities have the custom of making hakafot on Shemini Atzeret at night, to show that the two days are not actually two separate Festivals.) In Israel, where Simchat Torah is not celebrated on a separate day - since all Festivals are observed for a single day, the customs of Simchat Torah are observed together with those of Shemini Atzeret.
Simchat Torah comes on the last day of the festivities. At this time the last portion of the Torah is read, and since we never finish the Torah reading, we begin the reading from the very beginning again to show the Torah is beloved to us like a "new command to which everyone runs". This is a very happy occasion. All the Torah scrolls are taken from the Ark and carried in a parade around the synagogue seven times. We rejoice, sing and dance with the Torahs, for the reestablishment of our covenant with the Torah as a groom rejoices with his bride. For the Torah is betrothed to Israel as a wife is to her husband.
Children are given gifts of candy and fruit because it is stated that the "commandments of the L-rd are sweeter than honey."
The joyful dancing takes place the preceding evening as well as during the morning services.
