I've made two, one the hard way and one the easy way, IMO.
1. Curved piecing. If you do it this way, it's recommended that you put the convex piece on top of the concave piece, then sew the curves, which is fine when you're sewing the blocks together into rows, but when you sew the rows together, it means sewing it one patch at a time, then pulling it out of the machine, flipping it, and sewing another single patch, then flipping it again. What a pain. If you want to piece the curves, I recommend sewing the patches into blocks of 4x4 or something similar to start with, instead of long rows.
2. Applique. I found this way to be MUCH easier and less frustrating. I made a heat-resistant template, painted the seam allowances of the top and bottom (aka convex) curves of the patches with starch, and pressed them. Then I laid them on top of the seam allowance of the concave edges of the patches and stitched. You can use a blanket stitch or do a straight top stitch.
I hope this makes sense - I can add photos if that would make it easier to understand.