The appointments clause (Article II of the Constitution) provides for the president to nominate justices, with the advice and consent of the Senate for confirmation. Prior to a vote by the Senate, the Senate Judiciary Committee holds confirmation hearings. The first published report of Judicial Committee public hearings was that of the nomination hearings of Louis D. Brandeis in 1916.
Library of Congress Congressional Research Service (CRS) reports provide additional background information. (They are frequently updated, so double check for the most current.) Here is a selection, which can be accessed through ProQuest Congressional:
Library of Congress: Supreme Court Nominations: selected floor debates, votes, hearing transcripts and Senate statements from 2005 onward.
Library of Congress: Supreme Court Nominations Web Archive: blogs, academic articles, Congressional press releases, and media articles dating back to 2005.
The Supreme Court of the United States: Hearings and Reports on Successful and Unsuccessful Nominations of Supreme Court Justices by the Senate Judiciary Committee, 1916- : KF 8744 J8
GPO's Senate Committee on the Judiciary, Supreme Court Nomination Hearings, 1971 onward: Committee page and by justice
Research files of John P. Frank on U.S. Supreme Court nominations: Tarlton Archives
See also ABA's Standing Committee on the Federal Judiciary, which evaluates the professional qualifications of federal court nominees, including those to the Supreme Court.
For further related materials, search the TALLONS catalog by subject for:
C-SPAN Video Library has a series dedicated to footage of various Supreme Court Confirmation Hearings. The video clip below is a sample.