In some methods the name changes - e.g. Scrums Scrum Master - but the major responsibilities remain the same; deliver on time, to budget, to scope (at least the Must Haves) and to agreed levels of quality.

So where does the PM start. First they need to understand, own and drive the development process. Good agile development is in fact an extremely disciplined approach with upfront prioritisation, tight development cycles and heavy use of techniques such as TDD and continuous integration, without which the approach falls apart.

Second they must adapt their management style. The manager must agree SMART objectives with the team. It then becomes the responsibility of the team to determine how best to meet those objectives, and the manager to ensure they have the tools to do the job, and to remove any barriers or constraints to progress.

Third they must develop a deep understanding of the problem domain and a reasonable understanding of the technical architecture. Without this knowledge it will impossible to provide leadership, help the team resolve issues or challenge and negotiate with the development team and business users.

Fourth they need to become excellent negotiators, agreeing with the business representatives the relative priorities of what needs to be delivered, and then ensuring that development stops when the minimum functionality set required to realise the business benefit.