The most commen foods you will find in Russia are bread, potatoes, cabbage, carrots and beet. Russians love meat and to them, going with out bread is starvation but going without meat is poverty.
One of the most well known Russian dishes is Borshch. It's basically just beet soup.
Another dish that is very popular in Russia is Pelmeni, it's little pastry dumplings filled with meatballs. They can be eaten alone with sour cream and butter or in a broth or soup.