Start with the end game
Playing chess - soviet style

Don't believe too much in the rules. All lies in the particular situation at the board. (You can also read Russian Chess by Pandolfini to begin with)

Start with the end game
Agree here. Botvinnik recommended endgame study. I have Understanding Chess Endgames and a bunch of specific endgame books like Secrets of Pawn Endings and Survival Guide to Rook Endings since I know that endgame study is quite important.
Also read some classics like Soviet Middlegame Technique, My System, and Questions of Modern Chess Theory by Lipnitsky.

Yusupov's 9 volume series seems to be the gold standard for "Russian" style chess training. A little expensive, very difficult, but highly regarded. Here's a nice discussion of them and you could also do a "search forums" for other threads.
http://www.chess.com/forum/view/chess-equipment/yusupovs-chess-series
I want to play chess like soviets did back in time. What are your tips to achieve such training style and gameplay :D