The Freedom of Information Act (FOIA) is an American law that allows members of the public to obtain copies of classified documents by having all or parts of the documents declassified by order of a federal judge. The judge may refuse the declassification of a document if it is necessary for the document to remain classified because it affects national security. At least, that is in theory. In practice it has been very unreliable, if one group requests for a set of documents and gets them, it doesn't necessarily mean that a second group will be able to get them. If the government denies they've got the documents that you are looking for, they may not be telling the truth. It has been known for a government to deny that it has any documents on an incident yet they release some a few months later. (the CIA and NSA are a prime example!)
The best known use of the Freedom of Information Act is to (try) to obtain NSA documents relating to their involvement with UFO encounters and Majestic 12.