Case law is the law created by the written decisions of courts as they apply and interpret constitutions, statutes, rules, regulations, and other court decisions. The United States has a common law system, which is one in which the decisions of courts and the rules those decisions set forth are considered to be a source of law themselves, just like statutory law passed by legislature is.
A case generally starts out in the lowest level of a court system, often referred to as a trial court, where the facts are presented and the court makes a ruling. If one of the parties disagrees with the trial court's legal reasoning, they might appeal the decision to an appeals court, which can review the trial court's legal reasoning.
Case law research can be complicated because there are many court systems in the United States. The federal courts usually deal with issues regarding federal law. such as bankruptcy, copyright, or civil rights issues. State courts usually deal with local issues, such as criminal law, family law, or property disputes. However, for many legal issues there is overlap between the systems, and it is probably a good idea when doing research to check for applicable case law at both the federal and state level.