My RGB LED Stairs Illumination video

OP will have to give you the Bill of Materials and we aren't exactly here to babysit a development.

If you have absolutely no electronics prototyping or development experience at all, I fear you may make a newbie mistake. The club owner shouldn't be asking you, but rather some engineer nearby. Not that I doubt your ability, everybody is able to its just I don't want them to lose faith in you.

If you want to do this yourself, then I suggest looking into a few things before you try and tackle this as your first project.
Yes you have to read allll of this, but it will help you a lottttt so just bear with me.

First off, you need an arduino or some sort of arduino clone development board. Many recommend the UNO, and I do as well for you. Its the most popular and most simple one to understand.

When I started, my brother bought me this book and it helped immensly, I was gonna quit but this book helped make it pretty clear to me on how things worked.

It helped out a lot with describing the basics of prototyping with the arduino and coding and everything I needed to know to just get started.
That was 4 years ago, so it may be a little dated, but all the concepts should be the same.
There may be an e-book or a pdf out there of this book too if you can't find a bookstore that carries it or something.

If you can, get all the parts in this kit. The book is made to go along with a kit and it should work just fine with this one.

Don't buy that product unless you want less hassle and have money to throw around.
You can get all those components at websites like Digi-key and Mouser or even just eBay.

Notes about the above kit:
-The USB cable is USB-A to USB-B, like a printer cable kinda.
-The deluxe jumper wires are just Male-Male jumper wires
-There are two types of RGB leds, common anode or common cathode. Not sure which it is, so just get both
-Everything else is straight forward

Once you have gotten all that and have done a few of the stuff in the book, work look over some of these things.

This link is for the external IC, the TLC5940 16-channel PWM LED driver
http://playground.arduino.cc/Learning/TLC5940
Seeing as how you are new to this, i'll explain a bit. The TLC5940 is a 16-channel constant current led driver with grayscale correction. Basically what that means is that it can individually control 16 leds. It is commonly used with RGB leds, like in this project. NOTE: This driver sinks current, not source, so you will have to have common ANODE RGB LEDS. (If you don't quite get that, you will through learning from the book, and you can search google. its very well explained. If you do decide to stick around, you'll probably ask some questions and chances are, you will get a response from Grumpy_Mike. Hes very knowledgeable and he has a website. He explains things very nicely. Link : Tutorials. There you can learn what the PWM means.

You will also want to check out http://arduino.cc/en/Tutorial/ArduinoToBreadboard
This link is a little old, and refers back to the ATmega168, but it is still completely valid. This would be a more advanced thing to you, something you would do when you have grasped the arduino platform and basic electronics pretty well.
This project is a standalone project, in that it does not have a full arduino board integrated into the project. It is driven by the microcontroller it is just on its own board and is no longer dependent on the Arduino board to operate. You will need an extra ATmega328p to do this.

You will also need to look up analog inputs, that is covered in the book though.
There are a lot of things you need to know to get this done, and I hope the best of luck. You can ask any questions any time if you decide to pursue this. I hope you do, because it is really fun.