No, seriously, "no stitch" means "no stitch". Look at the shape of the beret and think how you'd draw it flat. It's like those world maps that look like an orange peel: something rounded represented on something flat. According to the directions, you work each section twice on each needle's stitches.
If you're not used to working in the round yet, try something quick and simple, like a cat toy or a Christmas ornament, and you'll see what I mean. You're going to work eight repeats of this chart, which will make eight sections that look sort of like the side of an American football with the bottom end trimmed off. This is a really beautiful beret and it's going to be well worth the trouble of figuring this out.
When you're done, to get the lace to show its best and make the whole thing look nice, you dampen the piece, stretch it around a dinner plate as if you were putting it on a (very flat) head, and let6 it air-dry. While it's not 100% necessary to block hats, it does make them look nicer.