Purchase a changing table converter top with a restraint strap to hold baby in place, and a contoured underside, as well as adhesive strips to prevent the converter from slipping. These can be found in most baby and children's furniture stores and many department stores.
Remove the adhesive strips and affix the converter top to the dresser or other solid surface you intend to use.
Cover the converter top with a waterproof cloth changing station cover (available in the baby department of most stores).
Ensure that the converter top is solidly in place before placing your baby on the surface.