Transparency
The primary requirement for a strong relationship between you and the staff augmentation partner is based on absolute transparency and clear communication.
It means that the staffing agency should be able to provide you with a well-defined documentation on what its exact role is and a complete transparent break-down of costs.
They should also be able to reply to your questions in such a way that they clear all your doubts on a high-level with minimal knowledge of existing hiring processes.
This helps engender trust & set realistic expectations.