You can do it the low tech or the hi tech way.
Low tech: Get a paper clip and find the 24 pin connector of your PSU. Stick one end of the paperclip into the pin that connects to the green wire (the only green wire outta all the wires) and put the other end in the pin that connects to the black wire directly next to the green wire pin. If you did it correctly you should be able to turn on the PSU (just check and see if the fan starts moving).
http://www.dvhardware.net/modules.php?name=Sections&sop=viewarticle&artid=5
Hi-Tech: Pull out and open up your PSU. Take off the casing and separate the molex wires from the 24pin connector wires. Again, find the green wire and the black one next to it. Snip off the green and black wires, and solder them together. You can then snip off all the other 24pin wires. If you do it this way, be sure to wrap the soldered wires in tape or shrink wrap so that it doesn't short out your PSU.
http://modfatha.com/building-a-test-power-supply-2.html
I'd also suggest that you use a PSU with an on/off switch so that you can manually turn on and off your new modded HDD enclosure. If you wanna get really fancy you could always try to reroute wires from your PSU to the front power button of your case so that it works to turn on and off your HDDs.