Main elements in Siberian dishes are pelmeni and bread - from (warm!!) breakfast to dinner. Pelmeni are small bags of dough - similar to Ravioli - and usually they are stuffed with ground meat, or mushrooms and potatoes. They are cooked with some broth and served with a lot of butter or sour cream (smetana). The sweet variety is filled with cottage cheese and eaten together with dessert. You can get it pretty cheap at any snack-bar or restaurant ("s smetanom" means "with cream"), or you can also find a frozen version in the market. There are different stories about the exact name, but latest news from Irkutsk have it that those filled with meat are called pelmeni and everything else is called wareniki.
Bread (chleb) is part of every meal, and concerning its taste, it is quite similar to German bread made of rye or mixed cereals. Not only does it fill you for little money but it also offers a perfect basis for having a friendly get-together with Vodka (see the section on drinks...).
Another specialty in all of Russia is called pirogi, dough-bags made of yeast and similar to rolls, which are stuffed with slightly fried cabbage (s kapustoi), mashed potatoes (s kartoschki) or ground meat (s mjasom). You can get them from the babushkas during the market hours - sometimes even grilled and warm - and also on the platforms of the TransSib.
Especially in the area around Lake Baikal, you should definitely try omul, a salmon-like fish that can only be found in the Baikal, and which is eaten either raw, cooked, fried, or - especially tasty - smoked. The fish stands in the market are therefore a rewarding point to visit. Furthermore, you can find fishermen's smoking stands in car parks, for example in Listvianka, where you can buy directly from their grill. During summertime, it's on your own risk for your health; during wintertime, it's no problem and definitely worth some frozen fingers.
Provided the housewife cooks right, you'll have several dishes. First, there is sakuski, i.e. starters - usually various salads or pickled vegetables followed by some soup, then the main dish with meat or fish, and in the end some sweet dessert. Often, there is even coffee or tea and chocolate served afterwards. In any case, you should thank the cook after the meal - vkusno is the magic word to use here; it means "it tastes well."