I've often thought that auto dealerships who offer the old "buy three get one free" tire sale are still making out like bandits, overcharging you for three new tires while throwing in the fourth for nothing. And I agree with everyone above; this is not something I trust an auto dealership shop to do.
I've bought tires at chains and at a couple local smaller shops and have had good experiences with both. If you buy from a chain store like Goodyear or Firestone, go online to price the tires, and either buy them online and select the shop where you want them installed, or arm yourself with the pricing information and just buy them locally, making sure you get the online price.
One big recommendation I can give you is to look for rebates. Often, you have to charge your new tires to the company's own credit card, but the rebates (usually in the form of a gift card you have to request after the purchase) can vary from $50 to $200 for a set of four tires, and when you use the card they also often offer same as cash terms for 6-12 months.