The Freedom of Information Act (FOIA), originally passed in 1966, generally provides that any person has the right to request access to federal agency records or information, and that agencies must give a written reply. As of 1996, the law also requires agencies to make some information freely available online, even without a specific request. (A history of FOIA legislation and changes is available from the National Security Archive at George Washington University.)
The FOIA does not apply to Congress, the courts, the central offices of the White House, or state or local governments. However, all state governments have their own FOIA-type statutes. This National Freedom of Information Coalition page provides resources to help with state FOIA requests.
Agencies are required to disclose any information requested under the FOIA, except for that which falls under one of nine exemptions or one of three law enforcement exclusions.
If you can't find information you want from the federal government, please start by contacting a librarian - we might be able to help you track it down. If it turns out you must file a FOIA request, the General Services Administration has a helpful brochure, "Your Right to Federal Records", which covers your rights under both FOIA and the Privacy Act. A more detailed guide is available from the National Security Archive at George Washington University.