The "TimesMachine" is the best way to search for historical articles from the New York Times.
The TimesMachine NYT archives search gives you a thumbnail view of that page of the newspaper where the article appeared. It is surprising how much information you get from the length and placement of the article on the page! This helps you easily separate little filler articles from actual news stories, so you can get to the content you want faster. Dates covered are September 1851 - December 2002.
A link to the TimesMachine appears in the footer of the NYT page in the "More" column. For articles published between 2003 to the present, click the magnifying glass icon at the top left to perform searches of New York Times content.
For this search on the D-Day Invasion, I narrowed the date range to a few months before and after the event. Click the "OK" button to apply that date range to your search, then click the "Search" button to get all the newspaper pages that mention your search term in that date range.
When a thumbnail image is selected, use the links in the sidebar to get a readable copy of the article in PDF format and to get a URL to this page with the Permalink option.