When looking for a paper I first look on line to see if it is available. If it is available for free I download it, if not I then look in my library's on-line catalog. If it is available on-line, but not in my library's catalog I request an inter-library loan (ILL). I have never been unable to obtain an article via ILL that was available on-line, but if I wasn't able, I would just buy the article. If it is in my library's catalog I go to the library and photocopy it.
If the article is not available on-line, I look in my library's on-line catalog. If it is available in the library catalog, I go to the library and photocopy it. If it is not available in the catalog I file an inter-library loan request. The success rate of these requests is lower than I would like.
If the article is not available on-line, in my library, and ILL failed then things get difficult. The first step is to email the authors. The second step is to talk to the reference librarian and see if you can find a library which is not part of the ILL service which has the paper. If you find one, talk to the librarian about how to obtain it.
My field also has a number of email lists where hard to find paper requests are not uncommon, it might be worth trying these. Similarly, you can ask colleagues directly if they have a copy. It might be worth doing a reverse citation lookup to find colleagues who have cited the paper (most people try and read what they cite).