There are a wealth of sources available through most libraries that will make finding material on Shostakovich fairly easy. There is one thing to keep in mind. Cyrillic alphabet words are rendered in a variety of ways into latin characters. See "A Few Considerations" for a list of possible spellings.
The number of results you retrieve from a search will be radically affected by the spelling you use. Some of the most useful"subscription" databases include:
Because of the diverse nature of the material, finding resources related to music can be very complex. Scores, recordings, musical criticism, video recordings are treated differently whether in a library or on the web. If you are just looking for some casual information you should have no difficulty using some of the general web resources available such as those listed in the left-hand column.
For more in depth information a good starting point is often a Music Library home page. The Music Library at the University of Illinois has some excellent guides to assist you in identifying databases, using the library catalog and the Music Library itself.
Music Research Resources are available at:
http://www.library.illinois.edu/mux/research/music.html
Research guides can be located at:
http://www.library.illinois.edu/mux/research/musicguides.html
It is also useful to use some of the Russian search engines when looking for either performances (podcasts or video) or to search Google Books and/or Google Scholar in Russian.
http://yandex.ru when searched for Dmitrii Shostakovich in Russian will return a link to a list of audio and video files of the composer's works.
There are many links to audio and video materials available online. If you are looking for Russian audio or video you might find Yandex the Russian search engine very useful. A search of Shostakovich brings up a great deal of material. The video file below was originally broadcast as part of a series entitled "Genii" and contains some interesting footage and commentary.
The Russians do not particpate in WorldCat, nor do they have a truly centralized union catalog of their publications. However, their national libraries and catalogs are superb. All of them have digitized materials that can be very useful. The Russian National Library has a series of specialized catalogs that are very useful. The Russian State Historical Library also has a specialized "Predmetnyi Katalog" which has its entries organized by subject. It is especially useful as it includes citatiions to articles.
For a complete listing of bibliographic sources in Russian see Resources for Russian Music and Opera at http://www.library.illinois.edu/spx/webct/SubjectResources/SubSourRus/artsrumus2.htm . If you are seeking Russian language articles on Shostakovich, published between 1956 and 1975 the article index supplement to the Soviet/Russian National Bibliography can be accessed via the web at: http://webapp1.dlib.indiana.edu/letopis/index.jsp .
Finally, for more recent publications, the Russian National Bibliography with all of its supplements is available here at the University of Illinois. This EastView database includes the Russian Music Index, Article Index and Index of Reviews. For those affiliated with the university it can be accessed at http://biblio.ebiblioteka.ru/search/search.do .