The Gemma M0 will be hooked up to the NeoPixel jewel via 3 wires. VOUT goes to PWR, D1 goes to IN, and G goes to G.
If you're happy using Gemma's onboard on/off switch (which is a bit tiny and hard to get to), that's all you'll need -- you can just plug the battery directly into the Gemma. If you go this route, remember to unplug the battery when the fascinator is being stored. The battery will slowly drain if it's left plugged in directly, and it's no fun to find a dead battery right before it's time to leave.
If you want to be able to turn the fascinator on and off more easily, and leave the battery plugged in during storage, I've also included instructions on how to add an on/off switch. It takes a little more soldering and time, but your hairdo will thank you later.