Often the New York Times article will link out to the original research they make reference to. When that is not the case, there are a few ways to search for the full-text.
The easiest thing to start with is to go to the journal's webpage (if the journal title is provided). If the publisher provides access to the research article free of charge, you are in luck! If not, try going to Google Scholar and using the Advanced Search (click on the three black lines in the upper left side of the page to reveal the advanced search feature). The Advanced Search allows you to narrow your internet search by things like author, publication and date. This is helpful in cases when the publisher does not provide free access to the article but it has been made available through other means (ex: author's website, National Library of Medicine database, an institutional repository). It's easier to do a more targeted internet search than to check all possible sites where the article could have been made available.
The other way to locate the full-text of a journal article is to check to see if UNO Library subscribes to the journal. Go to http://library.uno.edu and do a periodical title search in the library's online catalog. If UNO Library has a subscription to the journal you will see links to the electronic access or a call number for the print volumes.
If UNO Library does not have access to the article you need, we can probably get it for you from another institution via Interlibrary Loan. All current UNO faculty, staff and students are eligible to use ILL. The full cost for this service is absorbed by the library.