At the beginning of the game, the pieces are arranged as follows: for each side one king, one queen, two rooks, two bishops, two knights, and eight pawns. The pieces are placed, one on a square, as follows:

The rooks are placed on the outside corners, right and left edge.

The knights are placed immediately inside of the rooks.

The bishops are placed immediately inside of the knights.

The queen is placed on the central square of the same color of that of the player: white queen on the white square and black queen on the black square.

The king takes the vacant spot next to the queen.

The pawns are placed one square in front of all of the other pieces.

Popular mnemonics used to remember the setup are "queen on her own color" and "white on right". The latter refers to setting up the board so that the square closest to each player's right is white.

More Info: en.wikipedia.org