Step 1: Get the parts
4 CDs or DVDs (and if you're rich, you can even use Blu-ray discs or HD DVDs)
7 5mm White or warmwhite LEDs, I used warmwhite, because that I'm tired of the cold light, you get from the ordinary white LEDs. (I've posted some pictures, so that you can see the difference between the white and the warmwhite LEDs)
7 Resistors for the LEDs. I calculated, that my resistors should be 68 ohms. you can find a very good resistor calculator here.
Some electrical mounting wire. Should be the stiff type (the one with only one thick cupper conductor)
5 AA batteries preferably Duracell, cause they're the heaviest (the batteries are just there to act as a counterweight. Without them, the lamp would just tip over and fall).
A switch (optional)
Some ordinary hookup wire.
A USB male A connector with cord (I got mine from a broken webcam)
Some wire without insulation.