Lay the mirror on a flat surface, right-side down. Mark the bottom rail of the frame in two places with a chalk pencil, each about half the distance from the center to the lateral, or outer, edges of the frame. Mark both vertical portions of the frame about half the distance from the center to the upper edge of the frame. Precise measurement is not required.
Select a drill bit with a smaller diameter than the threaded shanks of the eye screws. Drill pilot holes into the thickest part of the frame at the levels of the marks on the bottom and sides of the frame. Be careful to avoid drilling completely through the frame.
Install an eye screw in each pilot hole. Turn the eye screws clockwise until the curved portions of the screws meet the wooden frame.
Thread the picture wire through one eye screw on the bottom of the frame from the center, toward the outside. Wrap the wire through the eye screw three or four times, then around itself. Thread the free end of the wire through the eye screw on the same side of the frame, then through the eye screw on the opposite side. Pass the wire through the eye screw on the same side of the bottom of the frame.
Grasp the wire that extends between the two eye screws on the vertical portions of the frame. Pull the wire taut toward the top-center of the frame. Pull enough wire to form a pentagon shape on the back of the mirror, with the top two or three inches from the top of the frame. Cut the picture wire four or five inches from the eye screw, leaving excess wire for attachment. Securely attach the free end of the wire to the eye screw.
Slide your thumbs under the upper portion of the wire, about four inches apart. Pull the wire toward the top of the frame. Mark the back of the mirror at the top points of the picture wire. Measure and note the distance from the marks to the top of the frame.
Mark the wall with a chalk pencil where you intend to position the top center of the mirror. Transfer the measured distance from the top of the mirror to the upper points of the installed picture wire. Mark the wall to this distance, below the first mark. Mark the wall two inches to each side of the lower mark. Hanging screws will be installed through these marks.
Drill pilot holes through each mark. If the bit meets a wall stud, stop drilling. The wood screw can be installed without a wall anchor. To install the winged anchor, pinch the wings of the anchor together, then pass them through the hole in the wall. Press the anchor firmly against the wall. If necessary, gently tap the anchor with a hammer until it is flush with the wall.
Screw the wood screws into the anchors, using a drill and driving bit. Stop turning the screws when they protrude about a quarter-inch from the wall. Lift the mirror by top of the picture wire with both hands. Hang the top of the picture wire on the heads of the wood screws.