Cut out one crown piece (7"x14" rounded, with long side on the fold), two brim pieces (3.5"x9" rounded, with short side on fold), and two brim pieces of interfacing cut the same as the brim pieces (med weight works fine). Note: The photo of interfacing shows them unfolded.
Iron your interfacing to your brim pieces
Stich brim, right sides together, leaving long straight edge open. Clip the corners, then turn brim right side out and iron 1/4" to 1/2" hem to the inside of the long open edge. This will to be to sandwich the gathered crown edge in before topstitching later. Note: It's a bit stiff at this point so you may have to pin the ironed hem while it cools to hold it in place.
Unfold crown and stich hem on the bottom (neck hem). If you want to put a neck piece on to shade the neck, do that instead.
Baste the unhemmed edges of crown. Your basting should go from one end of the neck hem up and around the curve and back down to the other end of the neck hem. Pull basting so that the circumference of the crown equals the length of the brim. The photo shows how to check that measurement with both items folded in half.
Once you've got your basting pulled to the correct length, tie off the ends (I use slipknots) so it doesn't scoot. Note: In this photo you can see the finished neck hem from Step Four.
Pin brim to crown, sandwiching the gathered crown edge between your ironed brim hem. You will use lots of pins to hold it in place. It should look something like this when you're done...
Sew along the brim where it meets the crown. Not too close or you'll lose the brim piece underneath in places. I stitch from the top because that's the part you'll see when you're done.
Add strings for tying. These can be fabric, ribbon, or whatever works for you. I handstitched some grosgrain ribbon on this one because it's faster than the machine work. It turned out like this:
Plus, I don't know if you can see it in that photo, but I added some elastic in the back of the neck so it wasn't so gappy, like this:
Well, that's it. How did I do? Did I miss anything or explain something poorly? It sure was easy to make, and now my other daughter is clamoring for her own, so I should go start on that one.