Knights can move 1 square in a horizontal fashion then 2 squares in a vertical fashion or vice versa. You could also call it 2 squares in a horizontal fashion then 1 square in a vertical fashion or vice versa. It can skip over pieces, but may not land on a piece of it's own color. It can however land on a piece of the opponents color - in effect capturing the piece.
Bishops can move any number of spaces in a diagonal fashion. It must stop either at the end of the board, one space short of a piece the mover owns, or on the piece of an opponents, in effect capturing the piece. Notice here the bishop captures the pawn in the previous picture.
A rook may move any number of spaces horizontally or vertically. But similar to the bishop, it must stop either at the end of the board, one space short of a piece the mover owns, or on the piece of an opponents, in effect capturing the piece.
A queen has the combined power of the rook and the bishop. It may move horizontally, vertically, or diagonally any number of spaces. Once again, it must stop either at the end of the board, one space short of a piece the mover owns, or on the piece of an opponents, in effect capturing the piece.
Notice the king is in check. This means a piece is attacking the king(in this case, the black queen.) The king must get out of check in one of three ways:
A. The king moves out of check.
B. Another piece comes to block the attacking pieces path.
C. The attacking piece is captured.
If the king does not get out of check - then the king is in effect captured and the game is over. Yes, the king is the most important piece in the game.
The king moves like a queen, except it can only move one space. It may not move the one space if it takes the king off the board, takes the king into check,(as a matter of fact, no move is permitted if it takes the king into check) or would land on a white piece. It can land on a black piece in effect capturing it.
A king also has a special rule - castling. This is the only way a king can move two spaces. What happens is the king moves two spaces left or right, and it's coresponding rook "leapfrogs" over the king. There are some castling rules however.
A. A king cannot castle if the king is in check.
B. A king cannot castle if the king goes into check during the castle. In other words, if the king is in check after one space of the castle, it cannot castle.
C. Because a king cannot move into check, castling is illegal if the resulting move puts the king into check.
Click here for other rules that you should know.