How do you write a design brief?

As a student, having received detailed and structured briefs from teachers and lecturers for several years it is an interesting concept to think of how this would actually work in the real world. Surely a contractual styled agreement that details the specific expectations of the business transaction from both the designer and the client would be a highly necessary thing.

So what is the best way to do this. The most desirable way would probably be to meet with the client where both parties could gain an understanding of how the transaction will unfold. After this it would be in the best interests of the designer to protect themselves and their understanding of the project by formalizing it in writing and submitting this with any further questions and perhaps a time line for progress and invoicing.