I ironed under 1/4 along the upper edge..
then pinned it to the backgroud..
As far as applique, you have many choices..
My choice is to thread baste about a quarter inch from the edge and blind stitch it down.. you can attach lace or other decorative edges before or after you apply the fan to the background.
If you are going to attach lace in the seam line, on top of the background, but under the fan, I would sew the lace to the fan with a 1/4 inch seam.. do this instead of pressing under the 1/4 inch. then when you turn the lace out, the seam will turn under.. pin and applique the fan in place leaving the lace free.
You could top stitch it down along the turned under edge
You could mark the edge with your pattern template and needle turn it under..again I would thread baste it down first...
Once the fan has been attached to the background.. turn the piece over and trim the fan to match the background.. you are done..
Congratulations