Veneer plaster is a thin sheet of plaster applied over another surface, usually drywall or plywood. Screwing into veneer plaster without chipping or cracking it requires a bit of thinking and planning. You need to know that once you put the screw in place, it’s probably not going to be removed, so be sure of your placement before you begin. Make sure you’re using the proper wall anchor for the weight of the item you want to hang. Take the time to do it properly and you’ll be pleased with the results.
Place a piece of low-tack painter's tape over the veneer plaster before you drill. This helps prevent the cracking and chipping of the plaster.
Put the screw that goes with the wall anchor you've chosen into the anchor opening and screw it into position. Make sure enough of the screw remains exposed to catch the picture wire or to slip through the key-hole opening on the back of the item you want to hang.