Get the parts and circuit diagram for this on http://learn.adafruit.com/
Print the buttons in using PLA filament for great light diffusion, and stitch the base pieces to your coat using regular thread.
Then, starting from the pocket, stitch power, signal, and ground connections between GEMMA and the chainable RGB NeoPixels using conductive thread. Don't sew them so tightly that you can't fasten the button, but not so loosely that the button can twist and short any connections.
To power the circuit, stitch a lipoly or alkaline battery pack into the coat's pockets. Code up your own unique color patterns and share your project with us on the weekly show and tell. Check out our full tutorial on http://learn.adafruit.com/