Sukkot is the third of the three "Pilgrim Festivals" in the Jewish tradition (the other two are Passover and Shavuot). While Passover is celebrated in memory of the exodus from Egypt, and Shavuot celebrates the giving of the Torah at Mt. Sinai, Sukkot is a celebration in memory of the huts in which Moses and the Israelites lived in the desert for 40 years.
According to the bible, Moses and the Israelites traveled in the desert for forty years before they were allowed to enter the Promised Land. During that time, they slept in shelters made of branches, which were relatively easy to construct and carry around with them. That is why the holiday of "Sukkot" ("Tabernacles") is celebrated until today.
Sukkot is also called "Chag Ha'Asif" ("The Holiday of the Harvest"), because it takes place at the time of year in which the crops were collected from the fields, and in ancient times some of them were brought to the temple.
The main tradition related to this holiday is building a Sukkah, a temporary home in which it is customary to live for seven days. In most places, Jews don't actually sleep in these huts, but eat their meals there every day. This also depends, of course, on the kind of climate you live in?
A second important tradition in Sukkot is hospitality. While traveling in the desert before entering the Promised Land, the Israelites were considered the guests of God, who looked after them and provided them with food and water. Therefore, Sukkot is a holiday of sharing meals and inviting in guests. This is also the basis for the custom of hosting the Ushpizin.
In each of the seven days of Sukkot apart from Saturday, it is commanded to say a blessing for The Four Species. Three of these species are held together in one hand, and the fourth (The "Etrog") in the other. Blessings for these species are said both in the Sukkah and in the synagogue.
On the 8th day there is no obligation to sit in the Sukkah, but it is still a holiday in which no work should be done. The uniqueness of this specific day is praying for rain. In Israel this is the time of year when winter begins, and since there is not much rain there, Jews started praying for rain as soon as Sukkot ended.
The 9th day of Sukkot is called "Simchat Torah" (meaning "The Joy of the Torah"). On this day the reading of the Torah is completed and begun again. During the celebration it is customary to circle the sanctuary seven times with the Torah, while singing and dancing.
In Israel the 8th and 9th day are celebrated together, whereas in other countries they are celebrated separately. The reason for this separation is that in the days of the Talmud, Jews who lived outside Israel couldn't know for certain when the first day of the month ("Rosh Chodesh") was declared, and they did not want to accidentally work on a holiday when working is forbidden. As a precaution they did not work on either of the two days...
The celebration of Sukkot begins on the 15th day of the Hebrew month Tishrei - 5 days after Yom Kippur - and lasts nine days (in Israel 8 days). This normally takes place in September, which is also the beginning of winter in Israel.