If you used Play Center, Google Play, Facebook or Twitter to sync your account you can then access it on another device. If you have not, and you still have the old device, its not to late to transfer, simply follow the instructions in this article.
If you already have a back-up of your old account and are trying to restore on a fresh game install simply use the recover account button on the initial account creation screen.
If you have an account on your new device that has passed the account creation screen you can enter the "Player Details" screen by clicking your player name in the top-left of the screen and logging in to one of the provided networks on that screen. This will allow you to restore the account on record.
Be sure that you select the correct option when attempting to recover a synced account! Selecting "RESTORE" will recover your previously saved racer, while selecting "OVERWRITE" will overwrite your previous saved racer with your current racer.