There's really not much to the project, hardware-wise -- the fun stuff is in the software. Power your controller and LED strip, and hook up the appropriate data lines between the controller and strip.
In my case, I'm powering the Particle Core via USB, and living dangerously by powering my LED strips right from the GND and VIN pins of my Core. Data is from pin A5 (could be any GPIO, though). I ran a power test using a 2600mAh USB battery, and it worked fine for about 2.5 hours. After that, I think the voltage dropped too low to overcome the forward voltage of the blue and green LEDs, so all the lights were red. It lasted about another hour in that state.
I've changed my code now with a lower default brightness level, fewer instances of blinking eyes, and I turn off WiFi. So the same battery pack should last a bit longer. I just need to do another real-world test.