You're basically setting up another tank to quarantine your fish. This is what most people do prior to introducing a specimen into their display tank to prevent a disease breakout with your current livestock and to get your specimen eating regularly to build strength and reduce stress.
It could be as simple as a 20-30 gallon tank (or depending on the size of fish), with no substrate or live rock. However I like to keep some in there to keep it as natural as possible, keep it cycled and running in case of emergency. Maybe a pvc elbow or tee for a hiding spot. A heater, HOB filter with carbon, powerhead, sponge filter, and light. Some like to prophylactically dose medications with Prazipro, like I do, and then treat with Cupramine if Ich is visible on the fish. Others dose immediately upon arrival. I like to wait a couple of days before treatment, get them to eat (with vitachem supplement), do a water change, dose the medication per the directions on the bottle.
QT period can be for 4-8 weeks depending on your confidence level that the specimen is healthy. Most people are strict at 8 weeks minimum or longer. Bottom line - get them healthy before you put a specimen in your display tank with fish that may be territorial and want to beat it up for fear of their food supply. This will get them acclimated to captivity better than dropping it in your display tank right from the get go. If they get stressed out they may go on a hunger strike and starve themselves to death. I've seen it happen first hand during my early years in the hobby.
BTW - just so you know this is to reduce the chance of spreading disease in your tank and to get your specimen as healthy as possible, but it's not always bulletproof. Some do a strict QT procedure only to have it still get some disease somehow, so keep that in mind.
