On the main menu, press Instructions. Select the Controls tab. On the provided screenshot, press the "Toggle Cockpit" quadrant once. Go back to the main menu, press Play Now, select your mode, and when you start up you should be playing in Darth Vader's TIE Advanced!
Millennium Falcon
On the main menu, press "Play Now." The next screen should feature the Death Star, an X-Wing, and options to select the Mission mode or the Arcade mode. Tap the Death Star's laser cannon port. Select your mode and you should be playing in the Millennium Falcon!