An increasing number of primary sources are available for free on the web. Here are some search strategies for finding them:
Strategy 1: To focus on primary sources, go to a search engine like Google, and combine your topic with terms designating primary sources such as memoirs, diaries, accounts, narratives, documents, autobiographies, online archives, correspondence, speeches. You can link synonyms together with a capitalized OR. Here are some examples:
Strategy 2: Another great way to find sources on the web is to think of a library, archives, or university that specializes in your topic, and pay them a "virtual visit" (check their web site for online collections). Researching the New York City draft riots during the Civil War? Go to the New York Public Library site and you'll find a great digital gallery with sources on your topic.
Please carefully assess each site you find, and be sure that the site was created by a credible author.
Most archival sources are still "off-line". However, archivists are digitizing many of their collections and linking them from their web sites to improve access, creating treasure troves of primary materials all over the web just waiting for history students to discover!
State Archives Collections Online lists some of the best digital collections in the United States.
Europeana is a massive archives created by European libraries.