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The point of the negotiation is for you to confer with your customer and produce an agreement what work will be done. You'll agree on the mutual conditions of satisfaction and produce an initial schedule with milestones and a statement of deliverables. Sucessful negotiation is --- in your abilty to be a good listener. As your customer is communicating their expectations, it is a good practice to "parrot" back what they are saying in your own words. The best way to make sure that your interpretation of the project is correct is to listen to your customer, show them your proposed solution and absorb as much commentary as you can. Everyone on the team should take notes during this proccess. By explaining your approach, you give your customer the opportunity to make helpful suggestions and clear up confusion early. Together you will describe such details as assumptions, schedules and deliverables. This negotiation officially initiates the project in some courses.
Remember also that you and your customer are still getting to know one another at this stage. Listen carefully to them and make note of their concerns.
The product of this negotiation is a promise to your customer to deliver what you say you will. If you believe that there is something that you can't deliver - say so. As they see you keeping this promise and completing the project, you will earn their trust.