Supreme court cases are availabe from many sources including the ones below. The best way to find a case is by citation (i.e. 347 U.S. 483).
A Brief is a formal written presentation of an argument that sets forth the main points with supporting evidence. Briefs are filed by both parties and often by "friends of the court" (amicus curiae). This term describes a person or organization that is not part of the lawsuit but has a strong interest in the case.
An Oral Argument is an oral presentation of a party's position before the court.