The simplest way to find court case results would be to look at the court docket after the case is over. The docket can be located at the local courthouse.
A court case has findings, proceedings and conclusions. To find out when and where a case will be, the docket is the answer for everything, including the conclusion of the case. If a conclusion must be known about someone else, the court docket can be found at the courthouse. However, there are many online sites that can be looked at to find out the results of a court case, and usually a local newspaper will contain information pertinent to the results of court cases.
Depending on what the court case was for and if the person wanting to know the results is the person that was in court, usually they will be notified by letter or by attorney. Some case results will not be notified by mail, and some can only be notified by attorney. Most states have a legal site that people can look at to find out recent court case results, as well. These sites are generally run by the state government or the same people that run the online site for the courthouse, and usually there is an online docket that can be viewed, although some of the information may not be available online. Federally, there is a "Public Access to Electronic Court Records" program that allows people in every state to check court dockets for results.