One way to find a primary source is to read through the bibliography of a secondary source. This is because a secondary source, if it offers an in-depth treatment of your topic, will mention speeches, emails, newspaper articles, court cases, first-hand accounts, treaties, etc. – some of which are primary sources. Once you find a primary source listed in the bibliography, your librarian can help you locate it on the shelf or online.
Here are some more tips:
In general:
In the library's research guides: consult the relevant research guide. For example, the American History and the World History research guides both contain a tab called “Primary Sources.”
Google / Google Scholar / Google Books: search for the topic plus the words “primary source.” Or search for the topic plus a word that indicates a primary source, such as diary, interview, correspondence, etc.