If the dealer is handling financing, they will get the payoff amount from the lien holder and have a check cut for that amount. That amount is tacked onto the new loan of the vehicle they are selling you.
IF you are handling the financing in any other way; you will have to place a check in the original lien holder's hand and get a statement that there is no lien, Then you can use the car as a down payment, sell it and/or us it in some other way with full ownership.