Here are the things you need:
If the seller has title free and clear, you need a bill of sale and the title signed over to your name (this varies by state but usually there is a place the seller signs and a place for the new owner's name and address. If you are in the same state, go to your DMV office to complete the transfer and registration paying whatever fees and taxes are required. If you live in a different state, you need to additional documents, A Federally approved state form from the sellers state stating the exact mileage and a limited power of attorney from the seller in case there are any issues in your state when you go to transfer title and register. You are then in a position to sign for the seller on any issue regarding the vehicle.
If there is a lean on the vehicle and the paper title is held by a lender, you will have to pay the seller the difference between the purchase price and the loan payoff and pay the lender the payoff amount. The lender will sign the title releasing the lien and the seller will sign over the title to you. Title and Bill of Sale, Federally approved milage form and signed power of attorney and you can take to your DMV to get the title transferred and the vehicle registered. (In many states you can take to AAA offices and they can do this for you faster). If the lender doesn't keep paper title but is a member in a state that allows lenders to keep electronic titles, the lender will release the lien and order a paper title from the DMV. Where they send it will depend on whether you are paying cash or you have a lender. If you have a lender, the lender will direct the lien holder where they want the title sent once they have submitted the payoff amount to the lender and specify that they are to be shown as the new lien holder. In most cases, your lender will have them send the title to you for you to register the vehicle. You need the same documents outlined above.
Lastly, to have Tesla transfer the vehicle to your account, you must request the transfer and they will send you an email telling you what information they require and copies of documents that prove you are the new owner (copy of title with your name filled in or the vehicle registration or temporary registration if your state allow for one.) Then you wait for Tesla to transfer the vehicle (claimed time is one week). They won't accept a Bill of Sale, only a title or registration with your name as owner.
Sorry for the long explanation but it is complicated.
