Re-varnishing a kitchen cabinet is a simpler process than a full refinishing job, and it's sometimes all you need to do to spruce up the surface. Full refinishing involves completely stripping, sanding and re-staining the wood. Re-varnishing alone is just a matter of dulling the old varnish surface enough to accept new varnish, then applying several layers of varnish, leaving the old stain intact. This shouldn't change the look of the cabinet, but will reinvigorate the shine.
Pull out the drawers. Use your screwdriver to remove the doors and take off the hinges. Set the doors and drawers on the floor, over spread-out newspapers. Remove all knobs, pulls and other hardware.
Set up your vibrating pad sander with 150-grit sandpaper. Sand the whole cabinet surface, going in the direction of the grain of the wood. Buff off the shine of the old varnish completely, but don't try to sand down into the wood. Use tack cloths to clean off the dust.
Brush on a coat of varnish, starting at the top of each cabinet and working your way down. Brush with the direction of the wood grain. Make the layer thin and even. Let it dry overnight.
Hand-sand the varnished surface very lightly with 300-grit sandpaper, just enough to dull the shine so the next layer will stick. Wipe with tack cloths.
Brush on a second layer of varnish. Let it dry, hand-sand it, then apply a third layer. Let the third layer dry for a full day before reassembling the cabinet.
Ventilate the room while using varnish.