Measure the width of the frame -- from top corner to top corner. Get a length of picture wire that exceeds this measurement by at least one foot.
Measure the frame's height, and divide this measurement by three. Measure down from the very top of the frame, using the length from the result. For example, if the frame is 12 inches tall, measure 4 inches down from the top. Draw a straight horizontal line with pencil, using the ruler across the back of the frame, to mark the measurement.
Measure the back lip of the frame. The back lip is the overhang from the frame on the back part of the frame, which is usually cardboard. Divide the measurement in half. Use the result to measure in from the end of the back lip on the frame's back cardboard, on the horizontal line you made. For example, if the back lip is 1 inch, measure in 1/2 inch. Mark the spot with the pencil, making a clear dot. Repeat on the other side of the frame.
Drill holes into the dots you marked. Make sure the hole is the right diameter for the clips' screws. Screw both clips in firmly with the screwdriver.
Thread one end of the picture wire through one clip, threading at least 4 inches through. Bend the wire where it meets the clip. Loop the wire through again and pull tight. Twist the leftover wire from the 4 inches around itself, as tight as possible. Repeat the process on the other side of the wire on the other clip, but trim any excess you have over 4 inches long, after you thread the other clip.
Lift the frame by the wire to make sure it's holding. Hang the frame on the wall.