Reference:
https://learn.adafruit.com/adafruit-neopixel-uberguide/best-practices
If you are connecting the Arduino to your computer and have a small strip of LED's, let's say <20, you can power them directly from the USB port:
Alternatively, with an Arduino UNO, you can power from the 7-12V input (preferably closer to 7). You could also provide a 5V power supply, and connect that directly to the 5V pin on the Arduino.
Make sure that ALL grounds are connected.