How to locate an obscure paper?

Locating the paper on MathSciNet is always a good idea: http://www.ams.org/mathscinet-getitem?mr=192581

First one should look at electronic mathematical libraries. Quite often they have an electronic version of the book.

Another efficient method is to look for papers that contain references to the paper under consideration and then ask the author of such a paper for a copy. In our situation a search reveals just one such a paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.9995&rep=rep1&type=pdf

Unfortunately, the author explicitly states that he was not able to locate a copy of the paper that we are looking for.

If all else fails, one should do a search on WorldCat to locate libraries that have a paper copy. In our case a search reveals quite a few libraries: http://www.worldcat.org/search?q=trudy+statistike&dblist=638&fq=yr%3A1960&qt=facet_yr%3A (When looking for a book whose original title is written in a non-Latin alphabet, one should be extremely careful in formulating the request. In our case the words “trudy” and “statistike” seem to be most resistant to distortion by transliteration systems used by different libraries, hence we enter them into our search query.)

Numerous university libraries in the US, France, Germany, Denmark, Slovenia, Czech Republic, Switzerland, Poland, and Australia seem to possess the book you are looking for.

Most probably your university has interlibrary loan agreement with at least one of these universities. Perhaps one of the libraries might be willing to scan the paper for you (maybe for some small fee), you might have a friend in one of these universities, or when traveling to a conference at one of these universities you can simply stop by the library.

Writing directly to Kovalenko (currently he seems to be affiliated with London Metropolitan Univeristy: http://www.londonmet.ac.uk/depts/cctm/staff-pages/staff-a-z.cfm) and requesting a paper copy should also be an option.

I have two related stories, one is my MO question:

Does anyone have access to a copy of Yury G. Teterin's 1984 (Russian) preprint "Representation of numbers by spinor genera"

The other was a 1930's article in Ukrainian, as I recall, that is not critical. I do not seem to have kept the email from that far back. Anyway, a friend of a friend of a friend was at a different university in Ukraine, and was willing to find the item and scan it in and email the pdf.

One thing I did wrong with the latter item (but chronologically earlier) was to try to rope a bunch of people into contributing to translating the item, including A. Eremenko at Purdue. That did not work and was not appreciated. So, a translation or part of one is a bigger deal, by far, than an article scan. My friend Dmitry read me selected sentences by telephone but indicated it gave him a headache, some words being uncertain anyway as differing from Russian. As clumsy as I was, this was worth doing, nobody knew about this article.

So I guess my summary is, people who have some involvement with mathematics are pretty generous about scanning in articles for people they will never meet. However, it does not do to get greedy with the kindness of strangers.

As for your last question: When I try to find "obscure" papers on the web, I mostly do a very broad search on Zentralblatt.

I tried searching for your paper searching for the Author, only to find out he has over >100 Papers (or perhaps multiple Authors with the same Name). Since you had the publishing year, finding the desired result was easy: Reference to paper

Sadly, in this case, ZB doesn't have a link to a free version of the paper.

But at this stage, I mostly have enough to go on to do a refined google search. In this case, however, this also failed.

Emil's comment would then be my next step, as well as asking Authors who have referenced the paper.