1. Pick the car you want.
2. Contact dealer 1 and ask for best price out the door
3. Contact dealer 2 and say “I want this car. Dealer 1 quoted me $X out the door. Can you beat it?”
4. Contact dealers 3/4/5 and repeat. Go back to Dealer 1 and repeat.
5. Arrange financing from bank/credit union, and buy from whoever gave you the best price.

Contacts can be done entirely by email.