You seriously think all the Sith are destroyed? Oh, dear. We need to educate you some more.
{Out of no where, my husband just started yelling, "No, stop her!}
Ahem. The Sith first appeared... Dang, actually, I don't know much of their history. There was a big battle in the early days of the Old Republic, and the Jedi Knights were formed.
With the Sith, there is a Master and an Apprentice. Darth Vader was the Dark Lord of the Sith - the apprentice. The Emperor was his master. Vader wanted to kill the Emeror, with Luke's help, and set himself up as Luke's Sith Master.
{Husband attempts to clamp his hand over my mouth.}
There were also other Dark Jedi at the time of Vader - I'm not sure if they were 'Sith' or just 'Dark Jedi.' For example - that cave in TESB, where Luke fights Vader/himself? Twisted with the Dark Side. Why? Because a Dark Jedi and Yoda fought there. (Yoda won.) The Dark Side acts like a molecule or some scientific thing, protecting Yoda from Vader. (When you get powerful Light Side and powerful Dark Side together, you can't see either. Magnets or something.)
{Husband suceeds in getting a hand over my mouth, but my fingers can still type... Bwahahaha!}