This sounds like a powerful technique. The problem is that I don't know how to give my opponent two weaknesses when they have none. Any advice?
Ideas I've seen are pushing the rook pawns and weakening the opponent's king or queen side. That's about all I've seen and know in giving weaknesses.
Pushing the rook pawns can be a powerful idea at the right time. But the reason you really need maturity is for big decisions like whether you should do a pawn storm, attack with pieces, or just choose quiet moves to improve and consolidate your position. The "principle of two weaknesses" is just a term for the concept that you shouldn't be so preoccupied with playing for a certain advantage (and perhaps even playing well for it) that you lose sight of a better strategical idea in the position. I like the example of Vladimir Kramnik vs Ernesto Inarkiev. Kramnik played the opening like Kramnik, starting out by isolating and weakening his opponent's queenside pawns, creating the first weakness. He was able to play a timely 16. b4, which made the problem worse, since the black c4 pawn couldn't watch over the b-pawn anymore. After forcing the knight trade on d4, he recaptured with the rook, and after the 24th move white is clearly better. But what I love about this game was Kramnik's move 26. Rg4! You rarely put your rook there. Kramnik was able to realize in the middle of a good position that the best way to finish Inarkiev would be to launch a tactically correct kingside attack, and he finished it off with a nice flourish. Inarkiev was a strong GM, what what sets Kramnik apart was that he was able to change his vision from the queenside to the kingside at a moment's notice.
[FEN ""]
[Event "Petrosian Memorial"]
[Site "Moscow RUS"]
[Date "2014.11.05"]
[EventDate "2014.11.03"]
[Round "2"]
[Result "1-0"]
[White "Vladimir Kramnik"]
[Black "Ernesto Inarkiev"]
[ECO "D53"]
[WhiteElo "2760"]
[BlackElo "2688"]
[PlyCount "79"]
1. d4 Nf6 2. c4 e6 3. Nf3 d5 4. Nc3 Be7 5. Qc2 O-O 6. Bg5 c5
7. dxc5 dxc4 8. e4 Nfd7 9. Bf4 b5 10. cxb6 Nxb6 11. Rd1 Qe8
12. Be2 Na6 13. Ne5 Nb4 14. Qc1 Ba6 15. a3 Nc6 16. b4 Bf6
17. Nf3 Bxc3+ 18. Qxc3 Qc8 19. O-O Bb5 20. Bd6 Rd8 21. e5 h6
22. Nd4 a6 23. Bf3 Nxd4 24. Rxd4 Bc6 25. Be2 Bb5 26. Rg4 Kh8
27. Qg3 Rg8 28. Rh4 Qd8 29. Qf4 Re8 30. Rxh6+ gxh6 31. Qxh6+
Kg8 32. f4 Bc6 33. Bf3 Qc8 34. f5 exf5 35. Qg5+ Kh8 36. Bxc6
Re6 37. Rxf5 Ra7 38. Qh4+ Kg7 39. Rh5 Qg8 40. Be4 1-0
When you say you want to apply " the Principle of two Weaknesses into your own game " then I will surely assuming that your rating should be at least 2200 Elo .
Now why I say this because there are rarely Games below this Elo level where you would find this principle being thoroughly applied . It is not that Players below this Level do not apply this but they do it implicitly without knowing that Principle of two Weakness is in consideration .Generally this particular methodology is applied mostly in End games where the battle is on both flanks or on two different positions and the Opponent gets subdued trying to control both and gets a catastrophic failure trying to shift balance on both sides .
You could see some Games from Youtube where you would understand this better .
Once you go through this link you will find many others with different examples .
