Definition: The Sith are an order of Force-sensitive beings who use the dark side of the Force. The first Sith character we encounter in the Star Wars films is Darth Vader, who, we later learn, was trained in the dark side by the Sith Lord Darth Sidious. The title "Darth" is an honorific for Sith Lords, and usually precedes a symbolic new name.
The Rule of Two
In Episode I: The Phantom Menace, Yoda says of the Sith: "Always two, there are. No more, no less. A master, and an apprentice."
He refers to the Rule of Two, which was established by Darth Bane around 1,000 BBY (and detailed in the novel Darth Bane: Rule of Two by Drew Karpyshyn). Bane sought to eliminate the self-destructive infighting within the Sith Order by creating an order in which only two Sith could exist at a time.
The Sith Empire
The continuous struggle between Jedi and Sith is one of the central facets of the Star Wars universe, and the Rule of Two version of the Sith in the films is only a part of it. The Sith began as a red-skinned, humanoid species which evolved on the planet Korriban around 100,000 BBY. Around 6,900 BBY, fallen Jedi encountered the Sith and helped found the Sith Empire, which stood until around 5,000 BBY. The beginning of the fall of the Sith Empire is detailed in the comic Tales of the Jedi: The Golden Age of the Sith.
The next great war between the Jedi and the Sith was the Jedi Civil War, which took place around 4,000 BBY and is chronicled in the Knights of the Old Republic comics and video games. Next came the New Sith Wars, between 2,000 and 1,000 BBY, which ended with the destruction of all Sith except for Bane. From Bane's Sith Order, Darth Sidious would eventually rise to become Emperor, with Darth Vader as his apprentice.
Beyond the Rebellion
In the comics Star Wars: Legacy, which take place around 130 ABY, a new Sith Empire rises to power under Darth Krayt. The organization of the Sith Order changed once more: these Sith rejected the Rule of Two, organizing instead into a Sith Emperor with many Sith minions.
Further complicating matters, the Sith do not represent the only philosophy of the dark side. Other organizations of dark side users include the Nightsisters of Dathomir, an all-female order of Force Witches, and the Prophets of the Dark Side, a religious cult. The Sith are still, however, the most prominent antagonists of the Jedi throughout the Star Wars films and Expanded Universe.