First Hyperspace War
Hundreds of years after the founding of the Republic, a group of rogue jedi rebelled against the council of their day. They felt that one should embrace emotion, rather than scorn it. These Jedi soon fell. The rest of the Jedi banished them into the unknown, and they disappeared.
These fallen Jedi eventually found the homeworld of the Sith race and quickly dominated it through superior mastery of the Force. But they had much to learn from the race and eventually their Empire took its name from the people they enslaved and eventually destroyed.
Many years later, scouts from the Galactic Republic stumbled across the Sith Empire and through cunning, luck, and internal politics, escaped and warned the Republic of the threat before the Sith could use the astrogation data in their ship to launch a surprise attack on the peaceful galaxy. In a series of naval battles, the Sith were defeated and eventually fell to internal power struggles before the Jedi were able to destroy the Empire itself. The TotJ comic books deal with this story.