Attach a twist drill bit to a power drill. Anchor manufacturers indicate the ideal diameter for drill bits on the anchor packages. If you cannot locate the manufacturer's suggestions, use a drill bit equal in diameter to the widest portion of the plastic insert anchor's shank.
Bore a hole through the drywall at the desired position of the wall mounting hardware, picture hanger or shelf bracket. Clean any loose drywall dust from the hole, using a brush. Insert the tapered end of the plastic insert anchor into the hole until the rim of the anchor's head butts against the wall's surface.
Attach a driver bit to the drill and mount a screw on the drill's tip. Manufacturers indicate the ideal screw size for an anchor on the packaging. If you cannot locate the manufacturer's suggestions, choose a screw that is large enough to grip the anchor's sides when driven, but not so large as to cut entirely through the anchor and split the plastic.
Align the wall mounting hardware's screw hole over the opening of the plastic insert anchor's screw hole. Insert the tip of the screw through the wall mounting hardware and into the anchor's opening. Activate the drill and slowly drive the screw into the plastic anchor. Drive the screw until it firmly secures the wall mounting hardware to the wall.
Attach a masonry drill bit to a power drill. Refer to the manufacturer's instructions to find the proper diameter of the bit, or choose a bit equal in diameter to the expansion shield's shank. Wrap a piece of electrical tape around the bit's shank to indicate the length of the expansion shield. The tape provides a visual indicator of the hole's proper depth.
Drill into the masonry wall at the desired location of the wall mounting hardware. Bore into the wall until the electrical tape meets the wall's surface. Remove the bit from the hole, and clean any masonry dust from the hole, using a brush. Insert an expansion shield into the hole.
Attach a driver bit to the power drill and a screw to the bit's tip. Align the mounting hardware's screw hole with the expansion shield's screw hole. Slowly but firmly drive the screw through the mounting hardware and into the expansion shield. Drive the screw into the expansion anchor until the screw's head secures the hardware against the wall's surface.