Write out a list of questions to ask the loan officer. This isn't a simple document. Some seemingly minor clauses can be expensive later. For instance, find out what happens if you want to pay the loan off early. Once your questions are answered it's time to negotiate.
Most newspapers list the rates charged by different banks and credit unions for auto loans.
Ask your bank if they'll match the lowest rate on the list. And don't concentrate on getting the cheapest monthly payment. Sure, you need to know that the payment is affordable. But a lower payment could hide the fact that you're actually paying more for the loan. That's a lot of money to give away.