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Topic: Corresponding Squares
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Wow, that Wikipedia description is almost incomprehensible. In simple terms, corresponding squares is mostly applicable in situations where only the kings can sensibly move and it says, 'If his king is on square A, mine must be on square B, or I lose; if his king is on square C, mine must be on square D; and so on.' These pairs of squares are the corresponding squares. Now, the point is that, if your opponent can get from A to C faster than you can get from A to D, you're going to lose.
I've used corresponding squares exactly once in my whole life. As it happens, it was in a friendly over-the-board game that I won, against a stronger player.  You can probably ignore it for now — as people have said above, knowing about the opposition and triangulation will be more useful for king and pawn endings; knowing the basics of rook endings will also be useful.
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JungJoe, you're a sweet bullet? How sweet? Very sweet, or somewhat sweet with a little sour tossed in? 
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Let us examine a relatively simple example:
WHITE: Kf4, d5-e6
BLACK: Kf6, d6-f5.
("White to play and win").
The plan to win is -believe it or not- the following: White king goes to the square g2 (for instance 1.Kg3 and 2.Kg2, or 1.Kf3 and 2.Kg2, etc- anything goes). Once placing the king on that square g2, the endgame is won.
Crazy? Of course this explanation sounds laughable- as long you don´t know the technique of corresponding squares.
Once you learn the technique, that plan becomes not just sensible but OBVIOUS. For this reason this example is so good to demonstrate the technique.
Before giving the solution (or rather, before explaining it), try yourself to find a way to win.
To start, observe that only White is hoping to win: as the White pawn on e6 is protected, Black can´t capture it because Black king can´t reach the 5th row because the "e" pawn would queen.
Now, observe that the difficulty of the position is due to White having the turn to move: otherwise (imagine it is Black to move) after 1...Kg6 2.e7 Kf7 3.Kxf5 Kxe7 4.Kg6, White wins (verify this yourself).
(to be continued)
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