In a nutshell, Legal briefs provide a summary of pertinent aspects of a case, an analysis of applicable law, and conclusion or advisement for the clients behalf--while in general a brief applies to a client in a court case, a brief can also be written as advisement to a governing body. In any case, a brief needs to identify the legal issues, present the facts and offer analysis (especially in the form of precedent) and a conclusion.
WikiHOW (yes!) offers a great example that walks you through how to write a Legal Case Brief. Scroll down the page for a step by step guide!
There are a lot of examples of the FIRAC or IRAC framework (Facts, Issues, Rule of Law, Analysis, and Conclusion) for writing Case Briefs. Some more examples are below: