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 arrest, trial, and lynching of Leo M. Frank was reported in American newspapers in the teens of the twentieth century, limit the dates in your search to the teens. Here are two screen shots that represent how to search this topic in the ProQuest historical newspapers.
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.