You can search the Web for archives. Many archives have an online presence.
Try searching for "Subject" (ex. "Abraham Lincoln" or "Toni Morrison") and "Archive" Once you find a web site, make sure you click on the 'About Us' tab and evaluate the credentials of the institution.
WorldCat, the world's largest catalog, is the best resource out there for locating archives collections.
As an example, see the Clarence Denman Papers, which belong to UTA.
Another excellent way of exploring archival collections is through ArchiveGrid's beta system from OCLC Research.
Another option if the student is interested in seeing which repositories might have uncataloged collections is to contact the SAA listserv (top option).
Finally, students can explore Texas archival collections via Texas Archival Resources Online (TARO).