Added Feb 2, 2013
First choose your fabric. Heavier fabric works better. Choose lining fabric.
Cut out 8 triangles of main and 8 triangles of lining. Place bill pattern on fold and cut 2 pieces. If using lighter fabric cut a stiffener slightly smaller. Cut the lining parts slightly longer to allow for turning.
For the band measure around your head, just above the ears. Mine is 21". Add about 1 inch ( for adjustments) Decide on width, allow seam allowance, and cut two strips. One strip will be against your skin so use a softer fabric if you want.
Next Step. Sew the crown parts together, 8 parts form a circle. Be sure to cut the curved triangles (not straight ones) this creates the shape. Don’t worry if the corners do not line up perfectly at the center. The button covers that. Now set the bill together. If using a stiffener you will insert it after turning. Now Sew the band. YOu will have two pieces, test fit it, baste if you have to. Sew the first part I call the inner band, together make sure it fits your head like you want.
Now that the crown is together, the bill together. Insert the bill between two layers of band. Again test fit, baste. I inset the bill about 1/4 in. Up to you. Once it fits like you want, stitch the bill inside. I laid the bands bottom edge facing the bottom edge of bill, sewed then turned and top stitched. Now you have a ring with a bill on it. Turn the band inside out and begin pinning the crown in place. It may be larger than the band, if so pleat it so that it forms little puckers.
Now turn it right side out. Sew the lining in the same way. There is not lining in the band. Turn and hem the bottom edge. Insert into cap and either whip stitch or machine it, again up to you. Choose a button that matches or compliments the hat and sew it in the center.
For the gray and blue version, I made the crown pieces about 3/4 in. longer and slightly wider. This gave it more of a muffin look.