Since the lights are DC, I don't think you need solid state relays. Just use MOSFETs. I recommend the IRF540N.

Is a triac like a transistor for AC?

I'm no expert, but I would imagine that you write code for processing to send info to the serial port. You connect an XBEE to an FDTI breakout board, which is connected to the computer.

Do you need help programming the Arduino?

[highfive/]

Just what I was going to say. Look at this- it will help

I am sorry you fried your Arduino. You don't need a capacitor; PWM is a pulse, if you add a capacitor it will absobe the pulse and there will be no dimming--full brightness.

The servo is connected to your Arduino, I presume you will be connecting strings from the fingers to the servo, like a pupet. Then you write a program for the Arduino to rotate the servo quite exactly. (Eg. 25 degrees left)

That's the spirit! I had a time when I would bring a bunch of electronic components and sometimes my Arduino to school and secretly experiment during classes.
Good luck!

http://flic.kr/p/dMXyLP
thats how to open a new tab

This is how to install Arduino drivers in Windows 8:
http://www.bryonconnolly.com/windows-8-arduino-driver-install
It got me trouble and for a while I'd use VMWare.
*EDIT* this is a better guide.
http://www.windows7hacker.com/index.php/2012/08/how-to-install-an-un-signed-3rd-party-driver-in-windows-8/

I remmember once trying to dirrectly drive a seven segment display with my Arduino and the segments were really dim I checked and found that I forgot to put

Code:

pinMode(segment, OUTPUT);

!

No. Upload the sketches in the photos linked.
http://flic.kr/p/dMX4Ri
http://flic.kr/p/dMX4RV

Have you tried uploading the example sketches?

My advice is to grab your Arduino and work through the simple examples on this site, such as good old Blink. Then grab a servo and a potentiometer and work through the two servo examples, namely Sweep and Knob.
I really think that to start, you have to get your mind how an Arduino program hangs together and how a servo is controlled.

Good luck!

You should use a piece of paper as a lamp shade to difuse the light. Then it would look nicer. Try not to make it la spotlight.