A board that is visually appealing makes you want to play more, I find.
Make sure you have the lighter colored square at your bottom-Right. It's just a convention, but it is the proper way. Pieces go on the row closest to you, and the pawns go in front of the pieces...
Pawns, prepared for duty!
You have a side, and your opponent has his own. Pawns can only move forward - unless capturing. If any pawn reaches the enemy's side it is promoted to a piece. Each pawn can therefore become a queen.
Now place your queen. She is the key offensive piece in the game; 2nd only to the king in terms of importance / priority. She starts on the square matching the color of her dress.
Your Queen, me lord. She moves in any direction, as far as she likes, back and forth. Losing your queen is usually catastrophic to your game, unless it's part of your overall plan for checkmate...
The King is YOU. You cannot capture a King, but you can attack it - putting it in "check". If it can't get out of check it is "checkmated". Game Over. 1 square moves, any direction, unless "castling".
The royalty needs a castle, or two. The rooks, or castles, are placed at the edges. They move in non-diagonal lines, as far as they can go, back and forth. These are your 3rd priority.
Horses, or Knights, are within the castle walls. They happily jump over pieces in bizarre L-shaped patterns, simultaneously attacking unconnected squares. Savages! Like bishops, they are 4th priority.
Finally, place the bishops alongside the royalty. Moving only diagonally, they stick to their original colors for the entire game. Yin and Yang.
All set-up! Now would be a great time to learn a couple classic opening sequences in chess. The Ruy Lopez is great for beginners who don't want to think too much too soon...