If you are a fan of horses you are in luck. Dig through your pile of chess men and find the two shaped like horses; these pieces are your knights. At the start of a game, knights are placed just inside of each rook. Knights are the pieces most likely to confuse a beginning chess player. Their move basically takes the shape of the letter "L." A knight can move in any direction - front, back, left, or right - two spaces and then an additional space to the left or right of that space. The movement can become beguiling because the final space is made relative to the direction you first moved. For instance, if you moved your knight to the right two directions your final one space would be made up or down in relation to the whole board. Any way you trace the movement, however, must look like the letter "L." A knight is also the only piece that can jump over other pieces. If a piece is in the path of a knight, it can jump over that piece. The only spot that needs to be open for a knight to move is the final space, for which you move one spot left or right. Knights, like rooks, capture pieces in the same way they move. If a piece is sitting on the final spot your knight can jump, it is in trouble. Remember, though, that it must be the final spot, not the spot you passed on your way to making the "L." This strange movement allows the knight to become a dangerous piece. You can often surprise an opponent with a knight.
Bishops
The pointy pieces in your set are the bishops. Each bishop is placed just inside the knights on the back row. Like the rook, a bishop can move as many spaces as you like. The catch is that they can only move diagonally. If you look at the initial setup, you will notice that one bishop is on a white square (or whatever the lighter color of your board is) and the other starts on a black space. Because the bishop can only move diagonally, each bishop must stay on the color on which it began the game. Still, being able to move as many spots as you like on a diagonal lane is a very dangerous weapon. Bishops capture pieces just like they move. If an enemy piece sits on the diagonal lane that one of your bishops occupies, you can move it to that space and remove the piece from the board.
Queen (the grand lady)
The matriarch of the board is the most powerful piece you employ. Not even the King himself can inflict pain like the queen. A queen's power comes from her mobility. She is able to move as far as you like in any direction. This fact means you can move the queen forward, backward, left, right, or any of the four diagonal directions, for as many spaces as you like. Often a queen can make it to almost any space on the board. Also, a queen can capture a piece on any square to which she can move. The rule for the queen's starting placement is "queen gets her color." For instance, if you are white, place the queen on the remaining inside square that is white. For black, place her on the remaining black square. If you look across the board, the queens should be directly across from each other.
King
As we discovered before, the king is the object of the game. The king shares some of his wife's powers, but he is far less powerful than the queen. A king can move in any direction, just like the queen, but only one square. The king is evasive, but his mobility is limited. While you generally want to keep enemy pieces away from your king, he can capture a piece by moving onto the square that the piece occupies. The king begins on the last remaining square of the back row. The inverse of the queen-rule is true for the the king. The black king will start on a white square and the white king will start on a black square. Again, like the queen, they should be directly across from each other.