The most cost effective way to get out a your car lease is to transfer your lease to another individual. There are lease transfer websites such as Swapalease.com that will list your vehicle for a fee to thousands of people interested in taking over a car lease. People who take over car leases want a vehicle for a short term with little or no money down. This method can save an individual $3000-7000 in early lease termination penalties.
If you take your vehicle to a dealership or car-buying service (such as CarMax or Carvana), you can trade it in on a new vehicle or outright sell it to them. The caveat is that you will almost always have negative equity (the value of the car is less than the payoff), that will be rolled into the new vehicle purchase or lease. If it is a sale to the dealership, you will have to come up with the money to cover the negative equity.
You can always call your leasing company(Audi Financial, BMW Financial, Merecedes, etc) and try to negotiate a turn-in price, however in most circumstances the leasing company will just try to collect your remaining payments or refer you back to the selling dealer.
Because the retail value of your vehicle is higher than a dealer will typically offer, if you can find an individual to purchase your leased vehicle, you may be able to mitigate some of the loss associated with your negative equity. Quite often, this could save you $1000-3000 off your negative equity total.
Although we do not suggest you do this, you can always stop payment on your lease and go into "default". This has many downsides such as the leasing company will still pursue the deficiency of the lease, as well as it will have a severe negative impact on your credit score. This credit rating decrease will make leasing or buying a new car through a loan very difficult to get with any of the major banks(ie US Bank) or automotive finance companies.