I just saws this: http://store.lightorama.com/cocori.html RGB led strip...

 can I use ardunio to build something like it? I am pretty new to ardunio but it seems like I should be able to copy some of the functionality of the cosmic color ribbon from that website. I am interested in making a tether for a weather ballon, say 50ft or so...

 Yes, you definitely can.  Search Instructables for "PWM LED."  PWM is "pulse width modulation," which is what causes the LEDs to brighten and dim.  You can program the Arduino to pulse different combinations of RGB.  Work it all out with a battery and 3 LEDs of different color.  

When you make the biggie, you are going to want to feed each pulsed signal into the base of a NPN transistor that can handle an amp or more for a LED array.  You will not want to run this off batteries because of the current drain for so many LEDs.  Get a 12v AC to DC converter that can give you several amps.  Run the LEDs off 12v, and have a voltage regulator that gives you 5 v for the Arduino.

You are going to find this an expensive project.  You'll save money if you buy LED strips with built-in resistors.  Search around the Internet for the best deal.