Primary sources are materials contemporaneous to the time you are researching, created by someone with first-hand experience of the phenomena that you are researching. Primary sources can come in any format, including newspaper articles, diaries, memoirs, letters, reports, scholarly articles, books (including works of fiction and non-fiction), films, artworks, laws, financial records, posters, photographs, and artifacts.
Archives are materials created by people or organizations, in the course of their every-day activity, which are preserved because of their historical significance or value for research. Another definition of archives: unique constellations of materials, collected and preserved because they contain important information and/or evidence of their creator's responsibilities and actions. All archival collections are comprised of primary sources, but not all primary sources are archival.
Because primary sources can come in any format, many databases and other places you would look for secondary sources are also good for finding primary sources. Examples of this include books in CLIO or HathiTrust and scholarly journal articles in JSTOR (which includes articles from the 19th century, helpful for researching the history of a given field or area of knowledge) or other databases. One way to find primary sources in these places is to limit by date to the period you're researching. Another is to use keywords (particularly in CLIO) such as memoir, autobiography, source*, documentary (which often refers to books of re-printed primary source materials), letters, etc.
In addition to the resources listed below, historical newspapers and other news media can be a great place to find primary sources from the time you're researching. See the News page of this guide for more on doing historical news research.
Some of these resources represent digitized archival materials from specific institutions; others are portals to multiple institutions' digital collections or databases collocating digital archival materials on a given topic. These collections include some formats highlighted elsewhere in this guide, including newspapers, government documents, and books; in addition, they contain manuscript materials (e.g. letters, notes, drafts of publications), photographs, and more. Archives are rarely able to digitize the entirety of their holdings or the entirety of a given collection; you should look to see full descriptions of collections on an institutions' website to get more context for digitized archival materials.
Start with ArchiveGrid.
This is a very short list of archival repositories that are close to Barnard's campus. For more help locating archival collections, navigating finding aids and scheduling research appointments with other archivists, or for an introduction to archival research, schedule a consultation with archives staff. You can also use the ArchiveGrid to search across finding aids and catalog records for archival collections in over 1,000 archival repositories, with some coverage outside of the United States. For non-U.S. archives in the Americas, I recommend the resources gathered by Archivistas en Espanglish (Latin America) and ArchivesCanada.ca (Canada).