To get to NYT or other news sources, go to the Library homepage.
At the main search box, choose the 'Journals by title' tab, and type in the title of the publication.
The link for the New York Times newspaper is the last in the list. When you click that link, the right hand side of the screen will then show which library databases holds that newspaper. The first link (click the title) is the easiest to navigate. If you click that link, you'll be taken to a page with the option to browse available content by date or to search within the publication.
It's worth noting that news access is sometimes challenging, particularly with flagship publications such as The New York Times. The Library has access to some of NYT, but not all of it (and this is generally true of news articles, as the copyright arrangements between journalists and publications sometimes mean that further syndication may be limited).
Please let us know if there is a particular article that you would like help to locate, or if you would like further assistance to locate other news sources.