Lease payments are actually quite simple if you can understand the lingo being used. Part of the reason why many people don't understand is because they are used to phrases like "interest rate" and "down payment". Technically, you're not buying anything when you lease, so they can't really call it these things.
Components of your lease:
Capitalized Cost = "cost of the car"
Cap Cost Reduction = "down payment"
Net Cap Cost = How much the car sold for after discounts and any money you put down
Money Factor = "interest rate"
Residual = How much the car is going to depreciate to at the end of the lease
Term = Months you'll be making payments
Sales Tax = 6.25% in MA
When calculating your lease, a dealership is still technically selling a car. The car is being sold to and paid for by the leasing company, which pays the dealership, and sends you your bill every month. Ultimately though, It is up to the dealership as to how much money they'd like to sell the car for.
Your payment is calculated using the following simplified formula, and subsequently billed to you each month by the leasing company.
( (Net Cap Cost - Residual) ÷ Term ) + (Cap Cost + Residual)
x Money Factor = Payment
((Price the car sold for - How much it will be worth at the end) ÷(Months)) x Interest Rate = Payment
With that being said, in an ideal lease, to get the lowest possible lease payment, you'd want to get a car that depreciates very litte, or one that the leasing company says depreciates very little, and get a HUGE discount on. This way, you are only paying for the difference between a highly discounted car, and an inflated residual value.