Adafruit the NeoPixels LED strip has three inputs: GND, V+ (or VIN) and DIN (or Digital Input). The ordering of the inputs may differ depending on when and who you order the strip from. Follow these steps:

1. First connect the capacitor and power supply in parallel.
2. Connect the 1000μF capacitor in parallel across the 5V power supply. If your multimeter supports capacitance measurement and 1000μF is within the measuring range, you may use it to verify the capacitance of your capacitor.

3. Connect up the grounds next. Connect the power supply ground to the LED strip ground, to the 74AHCT125 ground and the 10E pins, and to ground on the ESP8266. If you have a 3.3V supply, connect the grounds of the two power supplies as well.