Be sure you save all records of any repairs done, including receipts with dates of service and exact repairs done. This is especially important if your car was repaired by a mechanic other than the one at the dealership where you bought the car, particularly if you were physically unable to drive the car back to the dealer’s repair shop.
Keep purchase contracts, warranties, and repair orders to prove you have a lemon. (Don't keep repair orders in your car where they may get lost.)
In many states a dealer is required to provide a repair invoice for any service. Never leave a dealership without a copy of the service invoice. If the dealership refuses, you should write out the date and time the vehicle was at the dealer, along with the problem reported and ask an employee of the dealership to sign the document. If they refuse, write their name on the document and the fact that they refused to sign the document. You may also wish to mark on a calendar all days the vehicle is at a dealership for warranty repairs.