What is the best way to make sure that the customer will not ask for any thing out of the project scope?

The project manager needs to hold a meeting between himself and any interested stakeholders and customers. This meeting should be an open discussion which include information about project objectives, goals, constraints, scope, risks, costs, schedules, these topics need to be consistent with the project charter which authorizes the project by allocating the resources.

As the saying goes, the devil is in the detail. By ensuring the all the aspects of the delivery and requirements are identified initially, and which are aligned with the customers goals. Get these documented and signed off by the client with a very clear statement, stating that any other work outside of this will be constituted as a change and will be subject to additional budget, time etc.