The best online resource for finding Soviet archival material is the Electronic Library of Historical Documents:
https://docs.historyrussia.org/ru/nodes/1-glavnaya.
The website is in Russian, but most browsers successfully convert the page into English through their translation feature in the address bar.
The website features published Soviet archival material. Every document is fully transcribed, making the material accessible to everyone, regardless of language. If you do not know the name of the specific book you are looking for, the best way to browse is their “Historical period” page:
This will allow you to browse their collection of books, all the way from Ivan the Terrible to the Cold War. They have separate sections for the each period. For WW2 buffs, the most interesting periods will be 23 through 30 (the interwar period through 1945).
Recommended Reading
Naumov’s “1941 god” contains documents in the leadup to Operation Barbarossa, including Soviet war and mobilization plans, in 2 volumes:
The 1990s collection, “Russian Archives: The Great Patriotic War” contains a wealth of documents from the Second World War, organized by command authority (Stavka, general staff, etc.) and key battles (Moscow, Kursk, etc.).
Another valuable source is the “Collection of combat documents of the Great Patriotic War” published in the decade following the Second World War:
Archival Research 
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