After connecting to R2-D2 via the Star Wars Droids App, you will automatically begin at the drive screen. Set the aim by dragging the R2-D2 on-screen to rotate the physical Droid around.
When the physical R2-D2 is facing away from you, tap the Drive icon and a diving joystick should show up. Press and drag from the center of the joystick driving pad to the edge of the driving pad to get him to move. Move it all the way to the edge of the driving pad for top speed. When releasing your finger off the screen, place it anywhere within the driving area of the screen to regenerate the driving joystick to drive again.