Shovel the driveway to remove as much snow as possible from on top of the ice. A metal or metal-edged shovel may be able to scrape some ice off of the driveway while removing snow.
Chip the ice, if it is thick enough, into small pieces by striking the ice chipper against it with a vertical motion.
Shovel the chipped ice off of the driveway. Make sure to pile the ice where it will not melt and ice up the driveway again.
Apply a salt-free deicing agent. Calcium magnesium acetate is a salt-free compound that is more expensive than salt deicers but is less corrosive and less damaging to the environment.
Apply an enhanced radiation absorber such as graphite or coal ash. The dark material will increase the absorption of radiation and speed up melting.
Lay down electric heating cables or mats. Save for installation or placement, these cables or mats are low maintenance, require only electricity to function, and do not harm the surrounding environment with chemical or particle-filled runoff. This method may be most practical for walkways or a portion of the driveway that sees more foot than car traffic.