If you haven't already, Register for a free New York Times account.
Login to your account on the NY Times website.
Go to the TimesMachine website.
Search for a specific topic, person, or event. It can be helpful to change the dates to limit to a specific time period. For example, we can search for "man on moon" and limit our results to the weeks surrounding the moon landing on July 20, 1969. Note: Only articles published in the print edition from 1851-2002 are available on this site. For more recent articles, follow the instructions above to search the main NYT website.
Scroll through the results until you find the article that you want. In this case, we want the front page article that appeared on July 21 - the day after the moon landing. Click the article's thumbnail image. (Go ahead - click the image to read the article!)
Read the article. Use the menu on the left to navigate to the next page (if the article appears on more than one page) and to download a PDF. Note: You may only download up to 5 PDF articles per day
Also in the left menu are options to email a link to the article to yourself. You can also save the permalink, which is a shortened form of the URL. Saving this will take you back to the article.