Check

In the game of Chess, when a King is attacked or is in an immediate threat of being captured by any enemy piece, it is said to be in check. The player whose King is attacked must move him out of check by either placing the King to a safe square, or capturing the threatening piece, or by interposing a friendly piece between the attacking piece and the King (Fig. 1).

 White King is in check by the black Bishop:

The King must  get out of check by moving himself into the f2 square, or capture the black Bishop with the Knight, or interpose the f3 Pawn to the f4 square.

Fig. 1

There are several ways to put a King in check. The most common and very simple type is when a piece moves and directly attack the enemy King. The following diagrams show some other different ways to put a King in check.

Discovered check:
White moves his Bishop to d4 enabling his Rook to check the black King.

Fig. 2

Double check:
White Bishop moves to b5 allowing him and the Rook to check the black King.

Fig. 3

Skewer check:
White Queen moves to e3 checking the black King & captures the black Queen.

Fig. 4

Fork check:
By moving the white Knight to the f7 square, it checks the black King and at the same time forks both the black Queen and the black Rook.

Fig. 6

Discovered attack check:
The white Bishop moves to b5 checking the King and winning the black Queen.

Fig. 7

Perpetual check:
By checking  the opponent's King at e8 and h5 repetitively, the white Queen draws a game that had already lost.

Fig. 8

More about Check

When either King is in check and cannot get out of it with any legal move, it is said to be a checkmate and the game ends.

In order for a King to be checked or be placed in check, an opponent has to make a move so that one or two of his pieces attack the opposing King.

Check by two pieces is possible as shown above in the double check diagram. 

Neither King can directly check the opposing King himself, but a King can make a move which exposes the other King to a discovered check.

The Laws of Chess won't allow any player to make a move which puts his own King in check.

In casual games, a checking player can say "check" when making a checking move but is not required and it is no longer done in formal games.

Don't make useless check moves as it might provide the checked opponent a move opportunity or tempo to place his King into a safer position.

Checking an opponent's King might force it to move out of check and losing his castling option.

In descriptive and algebraic Chess notation, a checking move is noted like any other move and a "+"  sign is appended after the move, e.g. NB6+ and Nf6+.