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.