Frequently, researchers express a desire to explore a case, which may mean different things. Those interested in decisions as a matter of law will want the relevant case reporter for appeals of a lower court's decision. Those interested in the documents around a case at any level under any jurisdiction are engaged in a different research process. Much of what they do next depends on when and where the case occurred.
No one-stop site or resource exists for these alternately voluminous, scanty, or entirely missing case materials. If they survive, briefs, transcripts, and other materials may have been published or remain in manuscript in a local, state, or federal archive. Yale Law School's librarians have compiled an excellent guide for researching court records, briefs, and oral arguments.
HeinOnline provides a detailed guide for its Supreme Court Law Library. It also serves as an excellent introduction to the materials available for the Court's activities.