To determine the center of mass of a pinewood derby car, one effective method is to balance the finished car on a knife edge or hang it from a string at multiple points to find the intersection of the lines that pass through the center of mass. Calculating the center of gravity (CoG) for each component and summing them can also be useful. It is recommended to place weight as low and as far back on the car as possible to enhance performance. Additionally, minimizing wheel friction through proper lubrication is crucial, followed by considerations of weight distribution and aerodynamics. Overall, achieving an optimal design involves balancing these factors for the best racing outcome.