A primary source is an original source that was created at the time an event occurred. This is the generally accepted definition; keep in mind there are exceptions. Some primary sources, such as oral histories and memoirs, may be created after the fact.
These are some possible categories/formats of materials you might find. Of course, technologies available at the time of the event will determine some categories: Film newsreels are not going to be found if you are searching the Dark Ages!
Diary or diaries
Letters (note the term 'Correspondence' is the LoC subject heading subdivision)
Personal narrative (this is a LoC subject heading subdivision)
Journal (not the scholarly publication, but more like a diary)
Government reports and publications
Oral history transcriptions
Image or sound file
Paintings or drawings (may be a high-resolution photograph)
Music recordings and videos
Oral history recordings
Toys and games
Ephemera (items created for short-term or one-time use such as flyers, brochures, ticket stubs)
General Guidelines for Primary Source Research
Keep in mind that, as with all information, primary sources may be biased and/or incomplete. Editors, authors and compilers choose what to include and exclude. Memories become fuzzy or unclear, and are always subjective. All creators have bias.
In U.S.-based archives, you are more likely to find archives that reflect the dominant (white Eurocentric) culture. It takes money, time and physical space to create and collect archival resources, even if they weren't intended as such from the moment of creation.
When you find a primary source focused on a non-dominant group, examine it closely. Who created this resource? What was the power hierarchy between the creator and the subject?