The Circuit Playground must be connected to the "in" end of the LED strip. Data flows one way through the strip, from "in" to "out".
- Circuit Playground G --> Neopixel G
- Circuit Playground A1 --> Neopixel IN
The power supply will be connected directly to the strip, so power doesn't need to all flow through the Circuit Playground. Drawing too much current through a microcontroller can be problematic, so it's good practice to run the power directly to the NeoPixels if you have a long strip.
Connect the + and - wires from the screw terminal to both the NeoPixel strip + and -, and to the Circuit Playground's battery port.
Choose an appropriate power supply to support the number of LEDs you have. A small 2A power supply will work fine for up to around 60-80 pixels. If you have 150-200 like me, you may have better success with a 5A or larger power supply. Just remember that whatever supply you use, you must give the project 3.7-5V. Any larger voltage will fry your pixels, or a lower voltage won't be adequate to run them.
Head over to the Neopixel Uberguide to learn more about power requirements. For up to around 200 LEDs I found the 5v 4A power supply to be totally sufficient.