Al Lutz did a great job of describing the various combinations your journey may take. We are copying him here with minor corrections and adjustments. These are general spoilers, there is much for you still to discover on your own, even if you do read this spoiler box.
Each journey begins in the boarding queue where a pre-show will explain who your captain is and how C3PO bumbles his way accidentally into the cockpit.
You will then board the starspeeder and your adventure will begin. You'll find yourself setting out of the spaceport with C3PO trying to convince R2D2 to return for the real captain. It is at this point that you will experience one of the different plot twists, or “branches” as the Imagineers call it, which will begin the various storylines.
The 54 different versions of the ride are cycled through automatically, and they can slot in with any of the previous branches of plotline in any cabin. The various plot points and options are as follows;
Part 1: Your Starspeeder begins to depart the spaceport as R2D2 is trying to override the autopilot, but you are suddenly stopped by either Darth Vader or a battalion of Stormtroopers who are looking for a Rebel Spy suspected to be onboard your ship. The video screen in the cabin displays the image of one of your fellow passengers and sets up the base plot that they are a spy.
Part 2: After some fighting with Vader or the Stormtroopers, R2D2 jumps to light speed just in time and you are on your way to either Tatooine, Kashyyyk, or Hoth. You arrive at whichever planet the branching plotline led you to, and the typical mayhem and excitement ensues as you explore the planet. Tatooine leads to the obligatory Boonta Eve pod race, the Kashyyyk plotline involves racing Imperial Scout troopers on speeder bikes through the forest with help from friendly Wookies, and the visit to Hoth quickly devolves into an icy toboggan run down the mountains dodging Empire AT-ATs along the way.
Part 3: The action is brought to an end when R2D2 launches you off each planet and back into space where you suddenly receive a hologram transmission from either Princess Leia, Admiral Ackbar, or Yoda. They give you instructions on how and where to safely deliver the Rebel spy onboard, and with another jump to light speed you are on your way to a second destination.
Part 4: You arrive from the light speed jump at either Coruscant, Naboo, or an asteroid field that leads you to the Death Star. In typical WDI fashion, something goes terribly wrong here and you go through a final ordeal of either outer space dog fighting, dodging wrong way traffic, or fending off alien sea creatures. Each of these options leads to an obligatory happy ending with the spy satisfactorily delivered, and then you gather your belongings and exit to your right and out to the gift shop.