Unpublished Federal documents are acquired, organized, and stored by the National Archives and Records Administration (NARA). The NARA, as the name suggests, is an archive, and organizes documents, like other archives, by provenance. In the case of the NARA, provenance generally means originating agency.
Published Federal documents are distributed to libraries through the Federal Depository Library Program, and can be identified using the Monthly Catalog of United States Government Publications and also through library catalogs. These documents are published by the Government Printing Office (GPO), which is the largest publisher in the world.
For more help finding government documents, contact the Government Documents Librarian, Sanga Sung.
A note on Presidential Papers: Before the Presidential Records Act of 1978, all presidential papers were considered the personal property of the president, and presidents took their papers with them when they left office. The Presidential Records Act of 1978 designated any document produced during the course of the president's official duties (by both the president and his or her staff) as official, public records, and as such those documents become the property of the nation. Since 1981 each departing president has been required to deposit any such records with the National Archives and Records Administration (NARA). Most of these records now go to the departing president's Presidential Library, each of which (if it's an official Presidential Library) is overseen by the NARA. Their names notwithstanding, Presidential Libraries are more like archives than they are like libraries, and their documents are organized like archives. Bear in mind that these "presidential papers" will include a mixture of personal and official papers.