Ok, its absolutely simple, it really is.
The Falcon only needs 3 basic wires... Well, it needs more, but only 3 types.
12v - Only needs one of these
5v - Needs 3 of these
GND - 4 of these
Anyway, I will give you some basics
Here ( I hope the links are good ) you can see that the ATARI FALCON connector has only the mentioned coloured wires... The BLU is 12v, the RE are 5v and the BLK are GNDhttp://www.fatrakoon.co.uk/atari/images/PICT001.JPG
These can all be taken from any ATX PSUhttp://www.fatrakoon.co.uk/atari/images/PICT003.JPGhttp://www.fatrakoon.co.uk/atari/images/PICT004.JPG
Ignore the biro... Its only there to hold the connector down.
But you need to take the YELLOW from the PC and NOT the BLUE. The BLUE o na PC ATX PSU Connector is actually -12v and NOT +12v that the YELLOW is.
So, a small confusion there.
Anyway, a big bonus with the lfaon however, is that you can in fact avoid all the pins in that big connector and you can in fact use the Hard Disk power connectors instead ( Well, on a good PSU you can anyway )http://www.fatrakoon.co.uk/atari/images/PICT005.JPG
YEL = 12v
BLK = GND
BLK = GND
RED = 5v
Anyway, if you use an ATX Power supply, then you will need a way to force the power supply to switch on, and this is where the green party come in.
You only need to short the green wire to a black one.
Its best to use some switch on this, but for testing purposes paper clip should be ok.
I wont be held responsible for any mistakes I have made here... the Falcon is really esy to get forking with any AT or ATX PSU and even a child can do it, but mistakes happen, so double check everything.