Attach a masonry drill bit to a hammer drill. Attach the tape measure's tang, or clip, to the end of the bit and stretch the tape along the bit's shank. Find the desired depth of the concrete anchor's hole on the tape measure; refer to the manufacturer's guidelines for the proper depth and diameter of the hole. Wrap painter's tape around the shank of the bit to indicate the depth of the hole.
Press the bit's tip against the concrete and drill until the painter's tape reaches the concrete's surface. Remove the drill from the hole. Suck concrete dust from the hole with a shop vacuum or sweep out the hole with a soft-bristled brush.
Insert a concrete sleeve anchor into the hole until the anchor's rim rests flush with the concrete surface.
Attach a driver bit to a power drill. Press a screw into the hollow of the concrete sleeve anchor and hold the screw in place. Insert the drill bit's tip into the screw's slot and drive the screw into the sleeve anchor to expand the anchor and secure the screw in place.
Attach a masonry drill bit to a hammer drill. Stretch a tape measure along the bit's shank and wrap painter's tape around the shank to mark the desired depth of the anchor's hole. Bore a hole through the concrete until the tape reaches the concrete's surface.
Clean concrete dust from the hole with a vacuum or a soft bristled brush. Place a washer over the shank of the wedge anchor. Thread a nut onto the shank of the wedge anchor.
Insert the conical end of the wedge anchor, the end opposite the washer and nut, into the hole.
Hold the anchor with one hand to stabilize its position. While holding the anchor, pound the top of the anchor's shaft with a hammer or mallet. Pound the anchor until its hollow tip expands and grips the sides of the hole. Pull on the anchor to ensure that it is firmly seated within the hole. Tighten the nut with a wrench.