You cannot refinish veneer in the same way that you can refinish most solid oak furniture or cabinets. However, you can painting oak veneer for an effective result. Preparing oak veneer for paint is important for a successful paint job.
Make the veneer accessible. Remove the doors and drawers from the veneer cabinets or furniture. Use a screwdriver to remove the hinges from the doors.
Examine the veneer to make sure it is in good condition. If it is not, you may need to use wood glue to glue chipped or peeling pieces back into place.
Sand the surface of the oak veneer with #220 grit sandpaper and an electric sander. Be sure to get into the cracks and crevices of the cabinet or piece of furniture you are working on. Do this by folding the sandpaper over and using it to reach into the cracks of the veneer.
Remove the dust from the oak veneer by wiping it with a tack cloth.
Paint oil-based primer onto the oak veneer with a foam paint roller and a paintbrush. Use the foam roller on the large surfaces so you can avoid visible paintbrush strokes in the finished product. Allow the primer to dry overnight.
Spread semi-gloss latex paint over the oak veneer with a foam roller and a paintbrush. Avoid coating the paint onto the veneer in thick layers. Instead, apply a few thin coats of the latex paint to the veneer and allow each coat to dry to the touch before applying the next coat of paint.
Wait for the painted oak veneer to cure for three to four days before reassembling.