Determine how upside-down you are. The amount of negative equity you have will determine if you'll be able able to get out of the loan or not. Research your vehicle, using resources such as NADA and Kelley Blue Book to determine its value. Compare the value to your payoff. If you're only $1,000 to $2,000 upside down, you shouldn't have a problem. If your negative equity totals more than that, you'll have trouble getting out of the loan.
Attempt to trade in the vehicle. Trading a car in will net you less than selling it outright will; however, the dealer may be able to roll your negative equity into a new auto loan. Vehicles with large discounts and rebates will be easier to roll negative equity into; the rebate behaves like a down payment; it reduces the loan-to-value ratio of the new loan.
Attempt to sell the vehicle privately. Selling the vehicle privately will usually allow you to command a higher price, since you're "retailing" it instead of "wholesaling" it. If your payoff is drastically higher than the retail value, don't expect to get your full payoff. It's difficult enough to sell a car for the full retail price, let alone more.
Save up cash. If you can't trade in the vehicle or sell it privately, due to your negative equity, you'll have to save up enough cash to make up at least some of the difference between the actual value and the payoff. Once you can pay the difference upfront, you can choose to sell your vehicle privately or trade it in.