Tips for "current" news: look for resources providing full text access to their article content.
Tips for finding older news: News microfilm is analog. It is not searchable like a database, and has no front end search engine. Additionally, many of these microfilmed newspapers do not have a printed index to help isolate when a topic appeared in their press. So...how do you find articles on a subject ? By knowing the approximate date of events researched and browsing the paper around those dates.
Hint: If you don't know the dates, use the index of a paper that does have one, as a first step. Once you know when an event was being reported, browse your paper around the same time period.Often major newspapers, like the New York Times, do have an index. And a few, like the New York Times, have a searchable database for locating articles published in their paper [suggested resource: Historical Newspapers (Proquest),access path = Library homepage > Electronic resources > By type> News databases].