If its ich, you have to QT all your fish and leave your main tank fishless for at least 8 weeks to allow the ich to go through all its life-cycles and die out. Then you have to quarantine all new fish for 3 weeks or so to make sure it isnt carrying ich. However, most of us just live with ich in our tank. So long as the fish are in a low stress environment they usually dont show symptoms, and if they do get it they can usually fight it off - if they are in a low stress tank (ie not overstocked, correctly sized tank with good water quality) and continue to eat.
But for other parasites, like worms, fungal or bacterial infections you usually only quarantine the affected fish.