Many universities have digitized selections from their special collections as the UW Libraries Special Collections department has. Try a Google search with the keywords -- digital collections university -- to find other collections to browse.
A primary source is something you examine for clues about whatever you are investigating. Suppose my question is: did the mid-century spread of domestic refrigeration in the United States change diet and patterns of domestic work? I might look up old recipes, lists of what grocery stores sold, letters, or even photographs of people eating. Those would all be primary sources: artifacts produced in connection with the thing I am studying.
An archive is a collection of artifacts, and archival research involves collecting and assessing artifacts. The word “artifact” really just means “made thing,” and we use that term to emphasize that anything that someone has made can be used as a primary or archival source, depending on what question you are asking. Artifacts are generally produced by individuals or groups directly involved in the event or topic under consideration. Artifacts in archives may include eyewitness accounts, diaries, letters, speeches, works of art, films, photographs, songs, cartoons, illustrations, advertisements, recordings, government documents ... this list could go on. Archives are often created and maintained by institutions, but may also be private.
A secondary source, by contrast, is something written by someone else who asked the same question that you are asking, or a related question. One of the first things that I will do if I have a question is see whether someone else had the same question and tried to find the answer. So rather than plunge immediately into collections of recipes, I might see if someone has already written about the history of diet, cuisine, and domestic labor in the United States. Those would all be secondary sources. Think of secondary sources as co-investigators, friendly helpers. Even if you don’t agree with their answers, you can learn from their work.