Set your sewing machine to a wide zigzag stitch, and carefully sew around the entire perimeter of the butterfly wing. Keep the wire in the exact center of your presser foot, and double-check before you begin that the needle won’t hit it.
Stretch the fabric as you go, because you want your wing to be taut, and don’t worry about the excess fabric outside of the wing–you’re going to cut that off in a minute.
Your stitching should start at one “shoulder” of the hanger, up close to the hanging hook, and should end at the other shoulder. This will leave an opening, but you’ll need that opening in just another minute.
When you’re finished sewing around the perimeter of the wing, go ahead and cut off the excess fabric outside of the wing, being careful to cut close to your stitching without cutting your stitches. If you’d like to zigzag around the wing again to bind the raw edges of the cut fabric, then go ahead, but it isn’t really necessary.