There is no guaranteed best way to get a government document. Some sources I've found useful:
(1) The MetaLib, which simultaneously searches over 50 U.S. government document databases;
(2) The University of Michigan Document Center, which posts & links to many online government documents;
(3) The check the web site of the agency that put out the pub, or call the agency. Links to Federal agencies are posted on USA.gov. For Congressional publications, try calling the Legislative Resource Center (202-226-5200) and/or the House Documents room (202-226-5210). For other agencies, call the main number and ask if they have a publications department or a library;
(4) WorldCat and/or the online catalogs of Federal depository libraries. You can find depository libraries using the Federal Depository Library Directory.
(5) The GPO's Monthly Catalog of United States Government Publications (MoCat) lists all government publications published by the GPO since about the end of the 19th Century. Though the issues are monthly, the indexes are annual. The online edition MoCat, the Catalog of U.S. Government Publications, lists materials published by the GPO since 1994. Also, the U.S. Government Online Bookstore lets you look up government publications currently available for sale from the GPO.
(6) The Library of Congress holds lots of government docs, so you can use the Library's Online Catalog as a free way to search for government information. As far as getting materials from the Library, I don't know if the LOC would lend out government documents, but they do have a Duplication Services department (202-707-5640). Duplication Services is extremely slow, so you may want to find another source or hire a document retrieval service to go to the Library and make copies for you. (See the "Washington, D.C. Document Retrieval" entry.)
(7) State libraries are often the best source for their state's government documents. Large public and academic libraries often collect government documents for their state and local municipalities. County libraries often collect local government documents.
(8) Google. You probably searched Google before you even looked at this entry but, if you haven't tried it yet, give it a go now.
(9) Google Play sells electronic editions of selected Federal government documents.
(10) Government Attic stores government documents obtained with FOIA requests.
(11) E-book venders including the Apple iBookstore, Ingram, Overdrive, etc. sell Federal government documents.
Copyright: Some states assert copyright status in their government documents. The Harvard Law Library's State Copyright page summarizes the laws for each state (at least as of 2015; I don't know if this will be updated).
Questions: For questions about Federal government documents, you can "Chat" with or email a government documents librarian through Government Information Online (GIO), a "free online information service supported by nearly twenty public, state and academic libraries throughout the United States."