Aside from a university's own digital archives, you have several options to get copies of dissertations or theses.
A large fraction of the world's libraries list their holdings on WorldCat, and it's one of the first places I check for dissertations and theses. Ask your librarian if you want to get a copy of something on there via loan or look on your library website for interlibrary loan. I have received many dissertations via interlibrary loan.
You can also find many dissertations and theses listed on Google Books or HathiTrust, but they rarely can be downloaded. Google Books does not seem to have more than Google Scholar, but it provides links to WorldCat on the left side for each item. I often use both Google Books and WorldCat to do full text searches of books, and I sometimes find dissertations this way.
ProQuest is also a good source of digitized dissertations and theses. The service requires a subscription, but if you're affiliated with a US university then they probably have one.
Usually it's easier to find journal articles based on dissertations than the dissertation itself. So keep that in mind. I usually try to get both if the journal article is important as the dissertation often has extra details or tabulated data (compared against the plots in the journal article).
Few Russian libraries are on WorldCat. So, for Russian dissertations, I've found most I've wanted to be at the Russian State Library, but from what I understand you have to be present to read them, or have a library card to download more than the preview for the digitized ones. My university's interlibrary loan service has been able to get abstracts of these after many months of waiting, however.
One last option is to contact the author. I've done this many times and have received everything from no response at all, apologies that they are not able to provide a copy for technical reasons (old document format), to a copy of the dissertation or thesis in question.
Here are some related questions with other answers: