Decide on your search terms. This may seem a bit elementary, but by defining your search terms as narrowly as possible you will be more likely to find what you want quickly. This is especially true if you are conducting online research. For instance, if you are researching the newspaper coverage of the role William Jennings Bryan played in the Scopes Monkey Trial of 1925, searching under the term "William Jennings Bryan" will probably not be sufficient, since Bryan also served as Secretary of State and had been a Democratic and Populist candidate for president at one time. A simple search for "William Jennings Bryan" at Google News Archive Search will yield approximately 39,000 different articles from different periods in his life. It is essential to narrow your search to something more specific, like "William Jennings Bryan and the Scopes Monkey Trial of 1925."
Use multiple search engines, if possible. Google News Archive is one of the most extensive databases of archived newspaper articles available, but there are other good ones as well. Newspaperarchive.com and newslibrary.com both have searchable databases that are very helpful. Keep in mind that many of these sites require a subscription of some type to access the articles. Most of them will provide you with an abstract of the article but only allow full access for a subscription fee or a one-time fee for an individual article.
Know how to search the article once you've found it. If you are trying to be as efficient as possible, you can speed the process along by knowing how to use your browser's search functions. Once you have located your article, press "CTRL + F" on your keyboard. This will bring up a form to "find" any word or phrase you may be searching for. For instance, if you type "Scopes" and then click "Next," the browser will show you each instance where that term is found in the article by highlighting it.
Visit the local library or use your school's databases. If you are in college, you can usually rely on the school's library system and its collection of online databases to find newspaper articles. Familiarize yourself with each database and what newspaper collections it might contain. If you are not in school, you may be able to do much of the same research at your local library.