The 15th of Tishrei, which is in September or October.
The first day. (The eighth day, which is equally important, is actually not part of Sukkot.)
There are around 25 weeks (177 days) between the first day of Passover and the first day of Sukkot.
In 2009, Sukkot will be October 3rd to the 9th
The night of Hoshanah Rabbah (the evening entering into the seventh day of Sukkot).
Sukkot
The day proceeding the day of atonement is unremarkable except that there's an obligation to eat enough that one has an easy fast the next day. The day of atonement is during the month of Tishrei which has the following "special" days: Tishrei 1: 1st day of Rosh Hashana "New Year" Holiday. Tishrei 2: 2nd day of Rosh Hashana. Holiday. Tishrei 3: Fast day. "Tzom Gedalyia" Tishrei 9: Eve of Yom Kippur - mitzvah to eat, fast starts at sunset Tishrei 10: Yom Kippur - day of atonement. Fast ends at nightfall. Tishrei 15: 1st day of Sukkot. Holiday. Tishrei 16: in Israel: intermediate day of Sukkot - Hol Mamoed - half holiday. Outside Israel: 2nd day of Sukkot. Holiday. Tishrei 17: intermediate day of Sukkot - Hol Mamoed - half holiday Tishrei 18: intermediate day of Sukkot - Hol Mamoed - half holiday Tishrei 19: intermediate day of Sukkot - Hol Mamoed - half holiday Tishrei 20: intermediate day of Sukkot - Hol Mamoed - half holiday Tishrei 21: intermediate day of Sukkot - "Hoshana Rabba" - half holiday Tishrei 22: Last day of Sukkot. "Shmini Atzeret". Holiday Tishrei 23: Outside Israel: last day of Sukkoth. "Simchat Torah". Holiday.
Sukkot, in 2010, began in the evening of Wednesday, September 22 and ended in the evening of Wednesday, September 29
It starts on the fifteenth day of the Hebrew month of Tishrei, which occurs in September or October.
Sukkot in 2012 starts on Monday, the 1st of October and continues for 7 days until Sunday, the 7th of October.
In the wilderness (Leviticus ch.23).
Sukkot starts on the 15th day of Tishrei. In 2009, this corresponds to Oct 3rd. It continues for 7 days and is immediately followed by Shemini Atzeret/Simchat Torah.
Sukkot means booth or booths. Sukkot is a reference to our Fathers feast days, specifically the feast of Tabernacles which still stand today, and which have been eliminated by systematic Christian church worship. You will find our Fathers feasts given in Exodus, 12, 13, 23, 34, Leviticus 23 (all the timing given), and Deuteronomy 16The first is Passover (14 days after the spring equinox), 15th day is the feast of unleavened bread.The second is Pentecost (the feast of weeks) (50 days after Passover)The blowing of trumpets (first day of the 7th month)Day of Atonement (10th day of the 7th month)The feast of Tabernacles (in the fall on the 15th day of the 7th month) This is where Sukkot or the living in booths is defined as occurring during the Feast of Tabernacles (Leviticus 23:42). The Jews, continue this partially and call it Sukkot. The 7th month is what most refer to as September, its from the Latin "Septem" although the current days of September are not aligned with the days proclaimed and used by the Hebrews-Tribes of Israel. Sukkot or the living in booths as it is defined in Leviticus 23:42 lasts 7 days.