A QT tank must be cycled if the fish is going to live through the process. The easiest way to do this is to place a sponge filter or HOB in or on your tank or sump, which allows it to become colonized with the beneficial bacteria. This way, when you stick it in or on the QT, the tank is instantly cycled. I keep extra HOBs running at all times on my display tanks, and just keep the extra tanks for QTs in the shed, so I don't have to have a bunch of little tanks running all of the time and worry about keeping them cycled.
The size of the tank depends mostly on what you're QT'ing. I find a 20 gallon long a pretty good size to have around that works for most fish. Obviously, if it's a larger fish, you're going to have to go larger.
There's no need to use tank water in the QT. You can fill it up, dechlorinate it, and let it sit so that it either adjusts to room temp or, if you have a heater, allow the heater to heat the water to the desired temp. Then, throw on your pre-cycled filter.
Now you're ready to actually begin the process. Most people say you should QT for a month. This is really the safest. Be sure to acclimate your new fish properly in order to reduce stress as much as possible. Here's a link to to an article which includes tips for acclimation (it is based on SW, but much of the same info would be useful for FW):
http://www.wetwebmedia.com/acclimat.htm
While your fish is in QT, keep an eye on him. If you see signs of illness, find out what those symptoms mean, and treat for them. The only thing you might not see evidence of would be internal parasites, so it's often a good idea to go ahead and treat for them. Here's a link to Lupin's FW disease guide, which should help you identify illness:
http://www.monsterfishkeepers.com/forums/showthread.php?t=168667
And one to help you choose how to treat:
http://www.monsterfishkeepers.com/forums/showthread.php?t=137959
Don't rush QT. It will be tempting to throw your fish in the tank so you can enjoy it right away; however, your patience will pay off!