You can access the New York Times through several library databases, including ProQuest Global Newsstream. A quick way to get there is to click on Newspapers from the library website, like this
From the Newspapers page, scroll down to Select Newspapers and News Magazines and click on U.S. Newspapers in the Library to see the options. You can then choose New York Times or New York Times Online Edition.
Select Newspapers and News Magazines
You can then search within the New York Times, or browse by date.
Here are direct links to access these additonal New York Times publications through ProQuest Global Newsstream.
To access the New York Times for dates within 1851-2020, you can use the Historical New York Times database, which includes PDFs of the articles and full pages to see what they looked like when printed. See the library's FAQ How do I access the New York Times for a specific date in history?
If you need an article that is not included in the library databases, you can submit an interlibrary loan request.