When searching historical newspapers to find reporting on current events, it is best to limit the search to the dates most relevant to the event.  For example, to discover how the invasion of Poland was reported in American newspapers in 1939, plus the subsequent declaration of war by Britain and France, limit the dates in your search from September 1, 1939-October 1, 1939.  Here are two screen shots that represent searching in two different search interfaces:  ProQuest and Readex.

The skills you will employ to find articles in these two types of search engines will be transferable to other database search engines.

This is the search interface for the wide assortment of newspapers we offer via ProQuest Historical Newspapers.  This specific newspaper is the New York Times:

On the results screen, change the "Sort" option from relevance to oldest, so that you are viewing the articles in chronological order.  Also, since there are over 1000 articles, you may decide to select the option to look at the articles published just on the front page to get a sense of what was reported as important during the time:

This is the search interface for the newspaper collections we provide via the Readex search interface.  The specific collection is the African American Newspapers.

In this search engine, type in the word poland into the search box, and then type in the date range using the format required, in this case 09/01/1939-10/01/1939:

The results are displayed in chronological order, but because this is a collection of newspapers, you will see various newspaper titles are listed: