I made a quick copy of my Peter's headnet for a friend (without any crown elastic, which was too bad because it blew away unnoticed while it was pushed up off my face when I swapped with my friend). I didn't find it that hard to sew with a loose, long zigzag stitch if you aren't concerned about exact precision; I think it took me about 10 minutes start to finish. Ironing the tulle on "nylon" setting before cutting it out makes it easier to cut with any degree of precision.
A circular piece for the top, about a foot or more in diameter, depending on your hat brim, and a semi-cylindrical tube, widening at the bottom and several inches longer in front, with a drawcord at bottom front. Then sew the circle at the top of the tube. Add a row of stitches on that last (crown) seam to create a casing for a thin elastic cord if you want it to stay attached to the crown of your hat when it's pushed up off your face.