We know that the films opens with a space battle and that the start of the film signals the end of the clone wars (see theforce.net) so we can guess, probably quite accurately, that Dooku and the droids are fighting over Dooku's home planet. Dooku takes out a few Jedi, being an expert jedi pilot, but Anakin, in an epic shoot out, guns him down.
Sounds like a damn good start to me!
I wonder if Dooku realises his been betrayed by Palpy in those final moments?