Remove any doors or drawers from the cabinet in the location where you wish to install the dishwasher. If you are removing doors, use the drill and screwdriver bits to remove the screws. If you are removing drawers, pull them out to the end and then lift up on them slightly to release them from the track.
Remove the screws securing the cabinet to the others using the drill and screwdriver bits. These will be at the front and back of the cabinet, near the top and bottom. Remove any brackets that you see securing the back of the cabinet to the wall using the drill and screwdriver bits.
Remove the molding from the front of the cabinet at the floor, if any, using the claw-end of the hammer. Slide the cabinet section from under the counter top. You may have to lift up slightly on the counter top to slide the cabinet from under it.