It is important to understand the basic structure of the lease transaction if you want to get a good deal. There are essentially three components - the purchase price of the car, the residual value of the car at the end of the lease, and the interest rate (or, as they call it in leasing, the "money factor"). When you mention "purchase price", many car sales associates will look at you like you're speaking Greek. One said to me, somewhat dismissively, "there's no purchase price, this is a lease." Walk from these people and find someone better.
The dealer is selling the car to its finance company, but you have to negotiate the purchase price. They will take a trade-in on a lease, although as always you're not going to get the best value from the dealer on your used car. If you trade in, its typically best to get cash, not to use it as upfront money. Generally speaking, you're better off negotiating and comparing deals using a no-money down transaction. The residual value is probably the least negotiable part of the transaction. You are essentially borrowing the difference between the two numbers, so you want a low purchase price and a high residual. The money factor is the interest you pay on the amount you are borrowing. Good lease deals have interest rates very close to zero. Other factors you can negotiate are service agreements during the lease term (oil changes, etc.), and mileage adjustments.
