This question gets asked enough that I have an answer. If you can figure out what date the puzzle was published by puzzle name or author or whatever using the Puzzle Databases, then try any of the following three methods:
How to play with microfilm/fiche and get Sunday NYT puzzles
Go to the library and ask if they have the "New York Times Magazine" on microfiche, which are "plastic" cards the size of index cards" that have "pictures" of each page. That is the best source since the puzzle is in the magazine every week and you can go directly to the puzzle with little hassle once you are familiar with the reader. If not, you will have to ask about the "New York Times" newspaper on microfilm, which is essentially a short roll of film with pictures of the newspaper) which includes the magazine towards the end of the Sunday paper. Microfilm can be a little tedious at first until you learn the following trick.
Microfilm trick (don't expect this to make much sense until you've been on a microfilm/fiche machine)
The "black line" indicates a break between an upper and lower page. The magazine is much smaller than the newspaper and the microfilm process can fit two pages in where they normally fit one of the paper. Thus when you forward through the roll, the magazine stands out from the paper even at blurring speeds. Several times there are extra parts to the magazine (often devoted to fashion), so if all you see if fashion stuff, back up. Usually there isn't an extra part so the puzzle is nearly always towards the back of the magazine.
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