Opening the game

Keeping the following principles in mind may help you gain an advantage over your opponent at the opening.

1. Control the center
   Your pieces have the greatest freedom of action when they are in the center.  The most striking example is the Knight: a Knight occupying a center square commands eight squares, while in the corner, commands only two. 
   

2. Develop your pieces as quickly as possible. 
   This means moving all your pieces out so that they can act as one unit rather than isolated foot soldiers that can easily get captured.
   

3. Get castled as quickly as possible.
   Doing so protects your King and positions your Rook to strike.

Weighing what opponent piece to win

In chess, as in war, the side with the most force wins.  And force is proportional to material (or the number of pieces).  If you get ahead in material--mostly by acquiring enemy pieces, you should be able to win.  Chess pieces are not of equal value: the most valuable piece is the Queen, and the least is the Pawn.  Using the Pawn as the basis, we can assign numerical value to the other pieces (based on their ability to move).

How many pieces does it take to make a...