What are strategic elements for a correct piece sacrifice? I want know which plus elements need to have in general positions for a correct piece sacrifice! Or how do you know that a sacrifice is correct in complicated position?
There is no general rule for a correct sacrifice, however sacrifices are made with different ideas and strategies, such as, to get a huge space advantage, to initiate attack, to cause trouble to the king by opening up it's surrounding pawns, etc. But at the end you have to make sure that your compensation for the sacrifice is pretty good before you actually give up material, and that can only be done by precise thinking in the game. Some of the things you have to keep in mind before sacrificing your material are; 


You have good compensation for your sacrifice; i.e. you are gaining something back such as attack, space, gain back opponents material of same value or higher, or mate at some point.
You are defending loss of higher material, avoiding opponent's dangerous attack, defending mate.
Making sure of not going into a neutral position or causing no trouble to your opponent after giving up a sacrifice. This would just make you have less material for nothing.


Here are few examples of famous sacrifices, going through these kind of games will help you understand patterns of sacrifices and ideas behind it. (Make sure to read comments which will appear in the lower box of the game for most moves
) :

The strategical Exchange Sacrifice in Sicilian:

In the Sicilian Defense the exchange sacrifice on c3 is quite typical. In Dragon lines it is almost mandatory to sacrifice a rook for the knight on c3.

What advantages does black usually get? First of all, black gets a ruined pawn structure for white. Secondly, Nc3 was a defender of the central squares d5 and e4, and by eliminating it black can take over the center. Lastly and most importantly, black can launch a dangerous attack on the weak squares around white’s king, since Nc3 was the main defender of the queenside. All of these are major advantages that black gets in return for a material loss. The disadvantage of such an exchange is that if white successfully defends, white might just win because he is up on material. There is also a curious phenomena in such positions: sometimes endgames down an exchange favor black. This is because black’s pawn structure is compact and he usually has no weaknesses. There are no open files for white’s rooks to penetrate, making them not that active.

The following first example shows the attack that black gets for the sacrifice, while the next example shows the endgame.

[Event "WchT 4th"]
[Site "Luzern"]
[Date "1997.10.27"]
[Round "3"]
[White "Arencibia Rodriguez, Walter"]
[Black "Ivanchuk, Vassily"]
[Result "0-1"]
[ECO "B95"]
[WhiteElo "2550"]
[BlackElo "2725"]
[Annotator "Tyomkin,D"]
[Setup "1"]
[FEN "2rqk2r/1b1nbppp/p2ppn2/1p4B1/3NPP2/P1NB3Q/1PP3PP/2KR3R b k - 0 12"]
[Plycount "19"]
[Eventdate "1997.10.??"]
[Eventtype "team"]
[Eventrounds "9"]
[Eventcountry "SUI"]
[Source "ChessBase"]
[Sourcedate "1998.01.31"]

1...Rxc3 { Black destroys the main defender of white's king and sets
the targets of c3 and a3 for attack. } 2.bxc3 Nc5 { Black decides to bring his
knight to attack instead of taking on e4, even though taking on e4 gave black a
slight edge. } ( 2...Nxe4 3.Bxe7 Qxe7 4.Bxe4 Bxe4 ) 3.Bxf6 ( 3.e5 dxe5 4.fxe5 Nfe4 5.Bxe7 Qxe7 { leaving white with a weakened pawn
structure (a3,c3,e5) } ) ( 3.Rhe1 Qa5 4.Qf3 Qxa3+ 5.Kd2 b4 ) 3...Bxf6 4.Rhe1?? { Now black proceeds with his attack. White had to
be very creative to find the right defense. } ( 4.e5! dxe5 5.Nxb5! { the
point of e5, now Qd8 feels very uncomfortable under X-Ray from Rd1 } 5...Ke7! 6.fxe5 Bg5+ 7.Kb1 axb5 ( 7...Qb6? 8.Qg3 Bh6 9.Qh4+ ) 8.Qg4 Kf8 9.Bxb5 Qe7 { Tyomkin,D } ) 4...Qa5 { There is no way white can
hold this position together. } 5.e5 dxe5 6.fxe5 Bg5+ 7.Kb1 ( 7.Kb2 Na4+ ) 7...Bd5 { Black has a wide selection of ways to win. } ( 7...Qxa3 { Ftacnik } 8.Bxb5+! ( 8.Nxb5 axb5 9.Bxb5+ Kf8 10.Qg4 ) 8...axb5 9.Nxb5 Qa5 10.Nd6+ Ke7 ) 8.Nb3 ( 8.Qh5 { Ftacnik } 8...Qxa3 9.Qxg5 Na4 10.Bxb5+ axb5 ) 8...Qxa3 9.Bxb5+ axb5 10.Rxd5 Na4! ( 10...Nxb3 11.cxb3 Qxb3+ 12.Ka1 O-O ) 
0-1




    [Event "Sochi FIDE GP"]
[Site "Sochi"]
[Date "2008.08.14"]
[Round "13"]
[White "Karjakin, Sergey"]
[Black "Radjabov, Teimour"]
[Result "0-1"]
[ECO "B78"]
[WhiteElo "2727"]
[BlackElo "2744"]
[Annotator ",User"]
[Setup "1"]
[FEN "2r2k2/1p2pp2/p2p1bp1/q3n2n/3NP1b1/1BN1Q3/PPP5/1K4RR b - - 0 20"]
[Plycount "65"]
[Eventdate "2008.07.31"]
[Eventtype "tourn"]
[Eventrounds "13"]
[Eventcountry "RUS"]
[Eventcategory "19"]
[Source "ChessBase"]
[Sourcedate "2008.10.01"]

1...Rxc3!? 2.Qxc3 ( 2.bxc3 { staying in the middlegame might have been a
better option for white } 2...Qc5 3.Rh2 a5 4.Rhg2 Bd7 ) 2...Qxc3 3.bxc3 { at
this stage black would try to improve his pieces, bring his king up and start
pushing his pawn majority on the kingside to create a passed pawn there } 3...e6 4.Bc4 ( 4.Rh2 Ke7 5.Rhg2 Bh3 6.Rd2 g5 { doesn't give much to white } ) 4...Nxc4 5.Rxg4 { this trade does not improve white's position because now
black gets the c4 square for his knight } 5...Be5 6.Rg2 b5 7.Rf2 Kg8 8.a4 ( 8.Rhf1 Ng3 9.Re1 b4! ) 8...bxa4 9.Ka2 Nf6 10.Re2 d5 11.exd5 Nxd5 { now black
has perfectly placed pieces and three passed pawns on the kingside. While
before it was not clear who is better, now it is obvious that black is better,
since white has no counterplay. } 12.Rh3 Bxd4 13.cxd4 Nf4 { winning back one
of the exchanges } 14.Reh2 Nxh3 15.Rxh3 g5 16.Rg3 f6 17.Rc3 Nd2 18.Rd3 Ne4 { now the passed pawns decide the game } 19.c4 Kf7 20.c5 g4 21.c6 Ke7 22.d5 exd5 23.c7 Kd7 24.Rxd5+ Kxc7 25.Rf5 g3 26.Rf4 Kd7 27.Kb2 Ke6 28.Rxe4+ Kf5 29.Re1 Kg4 30.Kc2 g2 31.Kd2 Kg3 32.Ke2 a3 33.Ra1 a2 
0-1




EXAMPLES OF TACTICAL SACRIFICES

1- This game was played between Lasker, Emanuel vs. Bauer, Johann Hermann in 1889.
White sacrifices his double bishop to get a whooping attack on Kingside, and also sacrifices rook later in the game but to regain it and also win the game.

[Event "International Tournament"]
[Site "Amsterdam"]
[Date "1889.08.26"]
[Round "1"]
[White "Lasker, Emanuel"]
[Black "Bauer, Johann Hermann"]
[FEN "r4rk1/1b2bppp/ppq1pn2/2ppB3/5P2/1P1BP1N1/P1PPQ1PP/R4RK1 w - - 0 14"]

1.Nh5! { White threatens to
eliminate the king's only defender, and Black can do little to stop him. Bauer,
however, was still unperturbed: he figured that 1...Nxh5 followed by 15...f5
would nip White's shenanigans once and for all. } 1...Nxh5?! { Bauer must have
already written 15.Qxh5 on his score sheet, and contentedly leaned back in his
chair. As you probably already know, Lasker had very different plans. } ( 1...Rfc8 { This move would have been a real spoiler, as White must content himself
with an extra pawn and long-lasting attack after } 2.Nxf6+ Bxf6 3.Bxh7+! Kf8 ( 3...Kxh7 4.Qh5+ Kg8 5.Bxf6 gxf6 6.Qh6! d4 7.Rf3 ) 4.Qg4 { Of
course, Lasker would have had no trouble winning this position as well, but at
least Black could have avoided the double-bishop sacrifice. } ) 2.Bxh7+!! { A
devastating intermezzo. White gives up the pride of his position in order to
damage Black's kingside pawn shell and  -  more importantly  -  mobilize his
queen with check. } ( 2.Qxh5? f5! ) 2...Kxh7 3.Qxh5+ Kg8 { But what now?
The tempting 4.Rf3 is dreadfully slow, and after 4...f6 Black's king will
have a permanent escape route. Of course, Lasker has everything under perfect
control. } 4.Bxg7! { Snap! Crackle! Pop! Amazingly, White gives up another
bishop to destroy the pawn shell. Black has no choice but to recapture, but
his king is sent from the frying pan right into the fire. } 4...Kxg7 ( 4...f6 5.Bh6 Qe8 6.Qg4+ Kh7 7.Qg7# ) 5.Qg4+ { It is crucial to drive the king to
the h-file before mobilizing the rook. The immediate } ( 5.Rf3?? { let Black
off the hook: } 5...Rh8 6.Rg3+ { and now the amazing } 6...Bg5! 7.Qxg5+ ( 7.Rxg5+ Kf6 8.Qg4 d4! ) 7...Kf8 { turns the tables. } ) 5...Kh7 ( 5...Kf6 6.Qg5# ) 6.Rf3 { White threatens Rh3, and it appears that Black is defenseless. To
Bauer's credit, he is able to find an incredibly way to save his monarch from
instant death. } 6...e5! { A miraculous defense: Black's queen will give itself up
to stave off checkmate and eliminate the pernicious rook. As it turns out,
this merely prolongs the agony. } 7.Rh3+ Qh6 8.Rxh6+ Kxh6 9.Qd7! { If
not for this devastating fork, Black would have been very much alive. As it
stands, Black will lose one of his bishops, and White will then have a huge
material advantage in addition to a decisive attack. The rest is fairly clear
without comments. } ( 9.Rf1?! { would have complicated things after } 9...f5! ) 9...Bf6 10.Qxb7 Kg7 11.Rf1 Rab8 12.Qd7 Rfd8 13.Qg4+ Kf8 14.fxe5 Bg7 15.e6 Rb7 16.Qg6 f6 17.Rxf6+! { The last finesse. White crashes through and
wins even more material. It appears that Bauer was simply too shocked to
resign. } 17...Bxf6 18.Qxf6+ Ke8 19.Qh8+ Ke7 20.Qg7+ Kxe6 21.Qxb7 Rd6 22.Qxa6 d4 23.exd4 cxd4 24.h4 d3 25.Qxd3!? { This is some real chessboard sass!
Payback for not resigning, Mr. Bauer. } 
1-0




2- Here we will see a rare but important tactic: Interfering with the opponent's pieces.

White has two passed pawns which are close to queening. One is stopped by the black bishop, the other by the rook. White needs to sacrifice a bishop at the intersection of those two lines, forcing Black to decide which pawn to stop - and essentially "pick his poison". 

[Date "????.??.??"]
[Result "*"]
[FEN "8/3P4/4k2P/1B2B3/5K2/8/2b5/3r4 w - - 0 1"]

1.Bd3!! { Tadhaa! Sacrificing the bishop but intercepting both blacks Bishop and Rook. Black must capture this bishop one way or another - but either way, one of the pieces' lines will be closed, allowing one of the pawns to queen. } 1...Rxd3 { If the bishop captures the white bishop then the d-pawn will queen. Black could take the d7 pawn with his king, but then White will take the bishop on c2, and win with his passed h-pawn. } 2.h7 { If White played this before, the bishop could just take it. But now the pawns cannot be stopped since the bishop on c2 is blocked } 2...Rh3 { Black stops one pawn... but it's not enough to hold the position. Black had no way to open the bishop on c2, and stop both pawns from promoting at the same time. A truly amazing position! } 3.d8=Q { The rook could not handle both pawns on its own. In this lesson we have learned how to interfere with the opponent's pieces. In endgames, queening a pawn is crucial, and often it is worth it to sacrifice a piece for that end. } 
*




Source: Chess.com