From Westlaw:
A brief is a written summary of the case. To prepare one, you must distill the case's most important parts and restate them in your own words. The effort will provide a variety of important benefits. First, to describe a case accurately, you must read it carefully and thoroughly. Describing the case in your own words forces you to determine exactly what the courts said, which concepts and facts were essential to its decision, and the proper legal terminology and procedures.
Resources: "Why and How to Brief a Case" in Albert P. Melone, Researching Constitutional Law, pgs. 55-64.
The purpose of briefing cases is to train you to sift through the material you read and condense it to a manageable size. Since you will be required to discuss these cases in class, how you prepare your briefs will be critical to your effective participation. The most common errors in briefing cases are "overbriefing" (writing too many nitty-gritty details) and "underbriefing" (being so skimpy that you can't even recall what the case was about based on your brief.) A rule of thumb: one sheet of notebook paper filled on one side should be quite enough if used resourcefully (no skipped lines,etc.).
Caution: You MUST read the case in order to write the brief. You simply can't fake this assignment. I strongly recommend that you read and brief the case at one sitting. Do not put off writing it up as you are likely to forget essential elements.