In order to show off the CC3000 in the wiring diagram, I used the CC3000 breakout board. To make it easier on yourself, all you need to do is get the Arduino shield version and save yourself some wiring. With the shield in place, all you will need to do is wire up the NeoPixel ring's power, ground, and input. The input will go to the Arduino's digital pin 8.
Notice how I have the power for the NeoPixel ring going to the VIN pin on the Arduino. This is because I will be using a 5V power supply to power the Arduino, and this makes sure there is enough current to power the LEDs.