1. Go to "Preferences", and click on Board Settings".  Turn off reflections, shadows, transitions, bump mapping, antialiasing, and glare.  Realistic Shadows causes the biggest dip in performance, followed by complex shadows, reflections, glare, simple shadows, then bump mapping.  Antialiasing also eats up a lot of your processor's resources. 

2. If you have an older video card, run Windows in a 16-bit display mode instead of 32-bit display mode.  Right click on a free area of your desktop and select Properties.  Click on the Settings tab within the Display Properties.  On the Settings tab, you can change the colors of your display.  Choose 16-bit color and then launch the game.  This should allow more system resources to be usable by the Chessmaster program.