In most cases, the lender sends the funds directly to the private seller so you don't have to receive the money and pay for the car yourself. If you take out a personal loan, the funds are transferred to your personal account and you will have to discuss payment options with the seller yourself.
Possible methods of payment include electronic transfers using online banking or services such as PayPal, cheques, money order, cash or even debit/credit payments using portable debit terminals.