Somehow, the Emporer tricks Anakin into turning on the Jedi. My guess is that he convinces Anakin that the Jedi are responsible for Amidala's death. I believe her death will involve Anakin heeding Obi Wan's advice to "continue with the mission" like he did in Episode II when she fell from the shuttle but survived. This time, she ain't so lucky.
Anakin then proceeds to help wipe out the Jedi. All with the exception of Mace Windu who is beheaded by Boba Fett, just as Windu did to Fett's father in Episode II.
Anakin then discovers that he was tricked by the emporer and that he is really the Sith Lord Darth Sidious. The two then have the now cliched light sabre duel (what else?). During the fight, Darth Sidious' arm gets severed to reveal a mechanical arm. Just like Anakin and Luke. Anakin then is horrified to discover that Sidious is really his father and he invites Anakin to rule the galaxy with him as father and son. And unlike when Vader makes the same offer to Luke in The Empire Strikes Back and is rejected, Anakin accepts and completes his surrender to the Dark Side.
The surviving Jedi (Obi Wan and Yoda) at some point prior to this realize that Anakin's children must be spirited away so they can not be turned to the dark side. I suspect that they fake their deaths somehow. Leia of course is placed with the Royal Family and Luke is brought to Tatooine to live with Anakin's half brother ("They're good people. You'll be safe here" he tells Amidala in Episode II).
The final scene of the movie will be a shot of the Skywalker farm on Tatooine from afar where you'll see a young Luke Skywalker playing outside. The camera will pan back to reveal that we are watching the scene thru the eyes of Obi Wan Kenobi from a distant plateau. And thats how it will all end. With the slight hope for the fate of the rebellion in the form of this young boy, under the watchful eye of the last of the Jedi.