http://www.ladyada.net/products/pixel36mm/

Adafruit has a great tutorial on some square LEDs that I would like to use for a project. I have a regulated 12V 5A power supply that I would like to use. According to the instructions, it says to wire the power to the LEDs separate from the Arduino. My question is, how can I wire these things such that I do not kill either the LEDs or Arduino using a SINGLE power supply? I don't want two plugs hanging off the thing I'm making.
Thanks.