Upon completing the final level (The Pillar of Autumn), you will see a cut-scene of the ship taking off. When the cut-scene starts, hold your aiming stick (it will be dependent on your control scheme) so that you would "turn right" normally.
At the point when the UNSC shuttle docks at the Pillar of Autumn's landing bay, the camera will move to the right (if you were holding the stick to aim right) and catch a shot of a Spartan in a capsule. Should look familiar, right?