If your current car is not paid off, the dealership will look at the amount you currently owe on the car.
When purchasing a car, many people choose to trade in their current vehicle at the car dealership. If you don't owe any money on your current vehicle, the dealership will simply give you a credit, or trade-in value, for the car. The dealership might say your vehicle is worth $4,000 based on the make, model and condition of the car. In this case, you would then receive $4,000 off the purchase price of your new vehicle purchase for trading in your car.
If your current car is not paid off, the dealership will look at the amount you currently owe on the car. As long as you're not upside down on the car loan, they will be able to pay off the loan amount and (hopefully) give you a credit above and beyond what you owe. Let's say you own a car that's worth $15,000 but you owe $8,000 on it. In this case, the dealer would pay off the loan and give you a $7,000 trade-in toward your new vehicle purchase.