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 in articles about your topic during the time period--sometimes these terms are different from the language we would use today. One relevant example: many of the primary sources about the Whitechapel murders of 1888 do not use the term "Jack the Ripper." To search for these sources, you'd need to search for terms such as Whitechapel murders or the names of the victims.
Some databases allow you to limit your search to articles from a specific geographic area. Try doing this when researching events from 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. For example, you might come across "The Whitechapel Murders Papers: Letters Relating to the 'Jack the Ripper' Killings" by browsing Nineteenth Century Collections Online.