Subject searching a catalog for primary sources can lead you both to archival collections and to printed anthologies of primary sources. The latter might be complete enough for your research, or might serve as a springboard for further inquiry.
Any library record will give you a list of correct subject headings that you can use to find related materials, or you can view the Library of Congress Subject Headings to get started. Complex subjects often have subheadings, each separated by dashes. These subheadings tell you even more about what the resource is about. Example subjects with subheadings about Adams, John, 1735-1826 include:
These are just a few options. You can always broaden a search by removing subheadings; some subjects have as many as four!
To find primary sources, look for these subheadings with your main subject heading:
These subject headings may not be in the second position like the examples above, but further to the right in a longer heading. You can also try using these as keywords, so you can try something like "John Adams correspondence." This method works, but it's not as precise as the method of using the exact subject heading.
This also works with topics, not just with people. For example, if your topic has to do with World War II, you'll find that the official subject heading for that is "World War, 1939-1945". If you do a subject search in the catalog, you will find that subject headings with subheadings, including the subheading "sources". Thus, "World War, 1939-1945 -- Sources" refers to works that are compiled primary sources about the war.