Buying a used car. What should I do to get the best deal?

Buying a used car. What should I do to get the best deal?
Me and my mom are buying a used car and me being more into computers then cars, I dont know much. She wants a toyota corolla or camery with around 60,000 miles on it. We are going to a used car dealer. What kind of price should i ask for and what would be too much? thanks for any help!
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