Look at the information you have about the case.
Go to your local law library. Most counties have law libraries and all law schools do.
Search for a series of numbers and letters that look like this: 87 N.Y.2d 130, 637 N.Y.S.2d 964 (1995). This citation can be used as an address to find the case. It tells you two different books you can look in to find the case. In this example, look on page 130 of volume 87 of the New York Reports, second series, and you will find the case. The second address is volume 637 of New York Supplement, second series, page 964. 1995 is the date the case was decided.
Keep in mind each state calls its books different names, so you may have to ask a librarian what the letters stand for in your case.
Do you have just a name for your case? You will have to do some searching. It will help if you know what court decided the case. Each state has a digest series of books. You can look in the case name index and find out where to go to look up the case.
Consider doing an Internet search. Many cases are available online through law school sites or research sites such as FindLaw.
Go to the Jurisprudence set of books if you want to find a case about a specific topic but don't have a name or citation.
Ask the law librarian for help if you need it. That's why they are there.