Turn your hair dryer on the highest setting and point directly at the adhesive. Begin in the upper right corner.
Spray water generously on the area where you're heating.
Peel the adhesive away from the cabinet slowly as you continue to apply heat with the blow dryer. This method is the cleanest, but might not remove all the adhesive that remains after you get the contact paper off.
Pour soda directly on the adhesive if plain water and heat are not efficient. Leave on for a few minutes, then wipe off. On finishes that are easily damaged, test this method on a small inconspicuous spot first since the coloring in soda can stain the cabinet.