What did presidents do during their administrations? The documents and letters they place in their presidential libraries are a good start to find out. Recent presidents have libraries dedicated to preserving their documents, but a few earlier ones left their papers to institutions, historical societies and public libraries. See which on this NARA webpage.
Franklin Delano Roosevelt started the first presidential library in 1939 to house his papers and records for future research. Presidential libraries and museums have their own library system administered by the National Archives and Records Administration, a federal agency. Read more about NARA on their website, which is also a destination for research in and of itself.
The Barack Obama Presidential Center will be built in Jackson Park in Chicago's south side. Until then, the newest presidential library will be the subject of news stories, giving you a chance to read about all the considerations that go into planning one of these unique libraries. The building has yet to be built, but the website for the Barack Obama Presidential Library is up. Keep up with the latest developments here.