1) Start with your public library. Ask if they have old copies of the paper you want (specify time period). If they don't have it, ask if they can Interlibrary Loan (ILL) it for you, i.e., your library will borrow it from a second library in the same network, and you will be able to use it.
If all works out, you may be able to sit back and wait for the reels to be delivered to your library, for your use only (most of the time, for free, or for a very small fee).
2) If your library does not participate in ILL, you can check next with the publisher (see #3), but the publisher may be your last hope. Also, if your library DOES participate in the ILL system, but cannot find the paper, you will have to do the legwork yourself (see #3).
3) Check with the publisher: Obtain a recent copy of the paper you want to pursue. Write to the publisher at the address listed in the recent paper to see if they have old copies of the paper on microfilm- specify the time period in which you are interested (most publishers have old copies on film- or they make a deal with a specific library for the library to produce and store the film).
2) If the publisher has it, then you will need to ask them how you can go about to borrow the film. If a library has it (and if your local library performs ILL), find out the name and contact information of the library that is storing it.
3) Contact the library to ensure that the library does, indeed, have the paper you are requesting- and for the particular time period you are concerned with. Make sure that they will perform the ILL procedure for those reels.
4) Go to your local library with the information you've uncovered (still assuming your library performs ILL). Tell your library's ILL person that you would like to borrow such and such reels and that you've already done the legwork to find out where it is.
Your ILL person still may not be able to borrow your reels from the library you quoted, but it may give him/her another lead to continue looking for it.
Also, a word to the wise when dealing with ILL personnel, while ILL people are there to help the public, they generally don't deal directly with the public; they specifically deal only with ILL people from other libraries. And while most are generally friendly, please don't ask them to perform a direct loan from their library to your house- you might get snapped at- I've seen it happen! ;)