Try asking over at XtremeSystems.org forums. They'll tell you that you've got a lot of reading to do. That article you linked is useful though. You'll need: A condencer, a compressor, at LEAST a map gas torch, braising rods, you'll want nitrogen to purge the system while brazing, some HVAC grade copper tubing of the correct size, an evaporator - something found online or home made, someone to charge the unit for you or to get a hold of refrigerant and gauges and a vacuum pump or a couple old compressors to act as a vacuum. I've attempted a couple water chillers, using an old compressor as a vacuum and automotive r134a to charge the system. The results varied, but I'd consider them pretty good for just "winging it". You do need to be careful though, you'll be dealing with potential danger and the possibility of messing up the compressor.
I'd say an easy and good introduction would be taking an air conditioner and changing the AC evap over to a cpu block evap. You can order an evaporator that comes with the flex suction line, capillary line and mount, you just braze a couple joints, vacuum the system and then fill it or get it filled with the correct amount of refrigerant - which you may need to experiment with. Definitely do some reading though and ask the pros.