"You shall count seven complete weeks after the day following the holiday [Pesach] when you brought the Omer wave-offering. Until the day after the seventh week, [which is] fifty days, when you will bring new grain as a meal offering to G-d..."
Vayikra (Leviticus) 23:15-16 and 21

"This very day shall be celebrated as a sacred holiday when no work may be done, this is an eternal law for all generations, no matter where you may live."
Vayikra (Leviticus) 23:15-16 and 21

The Torah refers to the holiday of Shavuot with three names, Chag HaKatzir (the Reaping Holiday), Yom HaBikkurim (Day of the First Fruits) and Shavout (Weeks).

Unlike most holidays, Shavuot has no unique laws to set it aside from the others. We are prohibited from doing work like on any other Yom Tov, but we have no requirements beyond that, unlike Pesach for example with it's special prohibition against chometz.

Nevertheless, Shavuot has a number of wonderful customs. Most of them are rooted in the fact that Shavuot is also the anniversary of Matan Torah, the Giving of the Torah, at Mount Sinai.

The most well known custom is probably the custom to stay up all night and study Torah. We do this because tradition tells us the Jews slept late on the day of Matan Torah (so that they would be refreshed) and G-d had to awaken them himself. Today we stay up all night to make up for this.

Another custom is to eat dairy foods. One of the explanations given for this is because when the Jews received the Torah they learnt the laws of keeping kosher and the meat that they had available was no longer permitted to them. Milk and milk products however were not a problem.