Remove drawer pulls, door handles and knobs from the cabinets, using a screwdriver. Look inside the drawer or door to find the screw head. Turn the screwdriver counterclockwise to loosen and remove the screws. Set the drawer pulls, door handles, knobs and screws off to the side if you intend to use them later.
Take the doors off the hinges and pull the drawers out of the cabinets. Typically, screws hold cabinet door hinges in place. Unscrew the screws and set them aside.
Lay a fireproof blanket over your workstation to prevent damaging the surface. Place the door or drawer on the workstation.
Wave a heat gun back and forth along the edge of the door or drawer to reactivate the glue and make it tacky. Insert the tip of a utility knife into a seam at the edge and lift the veneer. Insert a thin wood slat under the lifted area. Continue to wave the heat gun back and forth to loosen the glue while pushing the wood under the veneer. Insert wood every 3 to 4 inches along the edge to prevent the glue from bonding the veneer to the substrate. Heat the glue and work the wood under the veneer until you've lifted all the veneer off the face of the door or drawer.
Position a heat gun along the edge of the cabinet base to soften the glue. Wedge a thin piece of wood between the veneer and substrate every 3 to 4 inches along the edge. Continue to heat the glue, wedge in the wood and lift the veneer until you've removed all the veneer from the cabinet surface.