You can find a court case by its title or case citation. For example: "Brown v. Board of Education of Topeka" is a case title. 347 U.S. 483 is the case citation for Brown v. Board of Education of Topeka. The citation reads as follows: volume, abbreviation of the name of the reporter containing the case, and page number on which the case begins. You can find this case reported in volume 347 of the United States Reports, page 483. (Reporters are law books that report court decisions in chronological order by jurisdiction of the court.)
You can also find cases in legal databases such as NexisUni. See the search widget below.