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. 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 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.
When looking historical newspaper and magazine articles, remember to look for articles published during the historical time period under study.