There are at least two different senses in which the term brief or legal brief is used.
An appellate brief is a formal legal argument written by a lawyer and submitted to an appellate court to persuade the higher court to uphold or reverse a lower court’s decision. It contains a summary of the facts of the case being decided, the legal reasoning behind the argument and citations of supporting authorities. An amicus curiae brief is an appellate brief submitted by a party who is not directly involved in the case but has a strong interest in the outcome. An appellate brief presents the legal issues in a way that favors one side of the case only. With the exception of U.S. Supreme Court briefs, these briefs are rarely published.
A student brief—or case brief—is a short, objective summary and analysis of a single case prepared for use in the classroom. It includes the facts of the case, the procedural history, the issue being presented, the judge's holding, the reasoning behind the holding, the rule of law upon which the holding is based, and a summary of any concurring or dissenting opinions.
These are resources for learning how to write a case brief.
Lawyers and scholars of the law have developed their own methods of citing legal materials in such documents as court briefs and law journals. Some other general style manuals have also developed specific rules for citing legal materials.