Visible Noise, you have a very interesting project (lasarium two ?). Each of the replies so far have been correct in the points they covered.

The diagram that Randal gave is universal driver (fan driver in your case). He didn't give values for the parts because they would change based on whatever parameters you might want to use (frequency tailoring, op amp used etc.) If you look at his diagram from left to right, the first part is a capacitor that would pass the AC (music) but block any DC that might get through. This protects his circuit from your amp and vice-versa, next is a diode that rectifies the music to DC, feeds it through two resistors an a capacitor that form a low pass filter that sums the rectified music into a variable DC (the loudness signal). So far the circuit is high impedance, meaning it passes very little current from the source. Next is a triangle, this is an 0p-amp configured as a buffer which gives the signal enough drive current to turn on your fan using the transistor at the right.

Keywalkers' circuit is a voltage doubler that is used in many power supplies. It's transformer that feeds a capacitor-diode bridge. The problem here is that modern day audio amps no longer use output transformers.

That 2200uf cap. passes the output to the speakers while blocking DC voltage from the output transistors in the amp. If you were to measure the voltage on its terminals when the amp is idle, the speaker side will be 0v and the amp side will be at half the supply voltage. The little tan 104 thing is a .1uf ceramic cap that stabilized the output of the amp.

Jack of all trades explained about the max voltage you'll get for your fans from the amp. That's from a 12v source. To get more speed you'll have to have an amp with a higher power supply voltage or get 6 volt fans.

I know I'm long winded but I hope this helps.