Briefing a case is a practice used by most law schools. On an undergraduate level, I have no reason to think the form would be any different. The idea is to provide a very brief summation of the identifying information and the high points of the case, which will help you grasp the facts and the principles involved, and which also is an aid to class discussion. Generally, what I recall from law school is this pattern:
Case caption - Provide the name of the case and its legal citations for example, Terry v. Ohio, 393 US. 1(1968)
Facts of the case - These should be very briefly stated, no more than one paragraph, and sometimes only a few sentences.
Procedural History - Explain how the case went from the trial court to the appellate courts that followed, who won and who lost at each level, who appealled.
Issues involved - What legal issue was involved on appeal?
Holding - What decision did the court make?
Rationale - Upon what did the court base its decision?
Disposition - Where does the holding leave the parties? For example, some cases are not done after the court makes a ruling because the case is remanded (sent back) to the trial court.
Concurring and dissenting opinions - Sometimes not everyone on the court agrees, which results in a dissenting opinion you are expected to briefly summarize. In other cases, there is agreement among the judges about the holding, but a judge or two (or three) will have a different reason for that decision and write an opinion explaining his or her point of view. This, too, should be summarized very briefly.
When I was in law school, we were expected to brief a case using only sheet of legal pad paper, sometimes for decisions that were more than sixty pages long. It is a challenge, but it can be done.
When I went looking to see if anything had changed, I found a link that I have provided below, which is exactly the way I briefed cases in law school. Once you get accustomed to this form, you will find it incredibly useful to grasp the essence of a case and to be able to discuss it intelligently in class.