If you are using a database with an Advanced Search form, try using the Advanced Search features to refine your search.
Since these databases cover many decades, it can be helpful to limit your search to a specific date range.
Think about what terms that might have been used to describe your topic during the time period. For example: the name of a specific person or organization or even a term that wouldn't be used today.
Some databases allow you to limit your search to sources related to a specific geographic area. Try doing this when researching a specific region.
These databases often sort results in chronological order. In some cases, it might be helpful to sort by relevance/best matches first.
In addition to searching, try browsing these collections to learn about sources that you wouldn't have necessarily thought of searching for.
These databases often display isolated sources, removed from any context. Explore available newspaper descriptions & other info to gather contextual information. For example, a search in the Library of Congress Chronicling America: Historic American Newspapers may lead to articles published in the Semi-Weekly Standard during the Civil War. The newspaper was published in Raleigh, NC, but you need to click on the newspaper description to find details about the newspaper's stance during the war. The publisher was a reluctant supporter of secession and wrote articles about "Federal gains across the South and the inadequacies of the Confederate government."