In the board game chess, each player starts with 16 Chess pieces. The moves of the pieces are defined by tradition, and by the international chess federation, FIDE. 

 1 king
 1 queen
 2 rooks
 2 bishops
 2 knights
 8 pawns

The bottom-right square of the board for each player must be white.

Summary 

Pawn - A pawn can only move ahead, to the far end of the board. A pawn is placed in each square on the second row away from each player at the beginning of a game, right in front of all of their other pieces, so each player begins with eight pawns. Most times, a pawn can only move to one square, the square in front of it. But a pawn that has not moved yet in the game can move ahead two squares, or just one. 

If an enemy piece is straight in front of a pawn, the pawn cannot capture that piece. Pawns have a special way to capture. A pawn can capture an enemy piece which is on the diagonal square to the left or right of the square in front of it. This is the only time a pawn can move to a square that is not straight in front of it.

If a pawn reaches the end of the board, it is removed and replaced by any other piece the player chooses, except a king or pawn.

If a pawn moves two squares on its first move, it may be taken (on the opponent's next move only) by an enemy pawn as if it had moved only one. This is called "en passant" (French for "in passing"). A pawn is worth 1 point.

Bishop - A bishop can move any number of squares diagonally, meaning, if you pretend the bishop is in the middle of a big X, it can move to any square along the lines of the X. Because of this, a bishop will be on the same color of squares for the whole game. At the start, a bishop is placed on the third from the left and third from the right of the row of pieces closest to each player. A bishop is worth 3 points. 

Knight - The knight is special because it is the only piece than can jump over other pieces. When a knight moves, first it goes two squares in one of the four ways a rook can move. Then the knight ends its move by going one square to the side. The knight is said to move in the shape of an L. See the picture (picture is coming). It "jumps over" the pieces on its way to its new square, and does not capture them, but the knight will capture an enemy piece if it lands on one. Knights are placed at the second and seventh squares on the rows closest to each player, between the rooks and the bishops. A knight is worth 3 points.

Rook - A rook can move any number of squares: left or right on the ranks, and up & down on the files.  Rooks start at the far left and far right squares in the row closest to each player, next to the knights. A rook is worth 5 points.

Queen - The queen combines the moves of a bishop and a rook. The queen is placed next to the king on a square of its own colour. Thus the two queens exactly face each other at the start. The queen is worth 9 points.

King - The king starts next to the queen. The king can move to one of the eight squares around it. It is limited as an active piece, but always is vulnerable to attack. No numerical value can be put on it.

A king may perform a special move known as "castling". This is when a king moves two spaces towards a rook, and the rook moves to the square on the other side of the king. This may not be done if: 
 there are any pieces (friend or enemy) between the king and castling rook
 either the king or rook have moved during the game
 the king, or any square the king moves through, is threatened by an enemy piece. The king must not castle into check.

References