The Federal Freedom of Information Act (FOIA) gives U.S. citizens the right to receive most non-confidential information from the government upon request. The act is codified at 5 USC §552.
You can get answers to basic FOIA questions (like how and where to make a FOIA request) from FOIA.gov. The answers to more questions can be found in A Citizen's Guide on Using the Freedom of Information Act and the Privacy Act of 1974 to Request Government Records (Second Report, 2005). Electronic versions of the Guide are posted on the Internet by Federation of American Scientists, the Small Business Administration and others. Also check out the DOJ Guide to the Freedom of Information Act.
LLRX published a series of articles on various aspects of FOIA. More FOIA information is posted by the National Freedom of Information Coalition.
The Federal agency responsible for FOIA is the Office of Information Policy (OIP). Lots of FOIA information on their web site, particularly the Guidance and Resources sections. Statistical information about FOIA is available on FOIA.gov.
Appeals and Litigation: If a Federal agency denies a FOIA request, the requester can generally appeal to a higher board within the agency. If that doesn't work, the requester can generally file a case in Federal District Court. Information on appeals and litigation is included in the Citizen's Guide and DOJ Guide referenced above.
E-FOIA: The Electronic Freedom of Information Act Amendments of 1996 (P.L. No. 104-231) essentially requires government agencies to post their decisions, policy statements, rules, manuals, etc. on the Internet. The Amendments were incorporated into 5 U.S.C. Sec. 552. See also E-FOIA Law Increases Access for the Public and Brings Changes to Agencies.
State Laws: States have their own FOIA laws (also called "Sunshine Laws"). Cites and links to these laws are posted on the National Freedom of Information Coalition's State Freedom Of Information Laws page. See also FNOIC's State FOIA Resources.