There are three different skins available for both the Prince & Elika, of which two need to be unlocked using a code. The final skin is unlocked via in-game collectibles (or by beating the DLC that we never got on PC...)

You can only change and unlock skins from the main menu. Navigate down to Extras and then to Skin Manager. From here, you'll see the option to switch between the Prince & Elika at the top, and the option to enter a Pre-Order Code at the bottom - this is, naturally, where you'll be inserting the codes.

Prince
This is the default skin which will already be unlocked and active.

Sands of Time
Enter the code: 52585854. This will also unlock Elika's Farah skin.
This will let you play as the Prince from The Sands of Time but without his never-ending thirst needing to be quenched at every water source you come across.

Altaïr
Enter the code: 13372805.
This will let you dress up as Altaïr Ibn La Ahad from Assassin's Creed. Hidden-blades sold separately.

Prototype Prince
Unlock by collecting all 1001 Light Seeds.
This lets you play as an early design concept for the Prince.

Elika
This is the default look for Elika which is already unlocked and active

Farah - S of T
Enter the code: 52585854. Will already be listed if you unlocked the Sands of Time Prince.
This makes Elika look like Farah from The Sands of Time, but on this adventure she won't "accidentally" shoot you in the back with arrows while you fight sand demons.

Jade
This should unlock on completion of the game.
This makes Elika look like Jade from Beyond Good and Evil, though without the ability to take photos.

Prototype Elika
This will unlock after collecting all 1001 Light Seeds.
This makes Elika go back in time to how she once looked during earlier development of the game.