You can find cases in a variety of different places.
In the olden golden days cases were only available in books called reporters.
Most states designate an official case law reporter which is published by the state government or a private publisher. The official reporter for Maine is the Atlantic Reporter, part of the West National Reporter System. The other reporter is West's Maine Reporter. Both reporters contain all published Maine Supreme Judicial Court cases.
Cases are also available online from the United States and Maine's judicial branch websites, from commercial services (Westlaw, LexisNexis, Bloomberg Law, LoisLaw, Fastcase, etc.) and from free websites (Google Scholar, Findlaw, LexisONE, Legal Information Institute, court sites, etc.). Beware, some of these sources include unpublished cases that cannot be cited as precedent!
The National Reporter System is the combined case law reporter sets published by West Publishing that includes all (published) state and federal cases.
West publishes U.S. District Court, U.S. Courts of Appeals, and the U.S. Supreme Court cases in separate reporters.
Federal Supplement - U.S. District Court (trial) cases
Federal Reporter - U.S. Courts of Appeal cases
Supreme Court Reporter - U.S. Supreme Court cases
State cases from the 50 states and the District of Columbia are published into seven regional reporters: Atlantic, North Eastern, North Western, Pacific, South Eastern, South Western, and Southern Pacific.
Approximately 30 states have their own individual reporters.
Note the citation formats for reporters in the middle column below. S.Ct. is the West Supreme Court Reporter; it is not official.