Very few LFS will QT their fish/corals. There's a couple out there that will for a small fee hold fish in a dedicated tank for 7 days for you. Even doing that there's an inherent risk of a new fish still being sick or carrying a parasite like ICK or Velvet. It is highly recommended to QT all new fish for at least 7-10 days (14 is better) before you consider introducing them to your main tank. You don't necessarily want to put the new fish into a QT tank treated with copper or some other form of medication unless there is a visible infection, but then why did you buy it if it was already showing signs of infection.
QT methods and treatment options vary depending on the fish their sensitivity to the various medications on the market, as well as what you are trying to eradicate.
The safest overall method is tank transfer as it uses no medications to treat the fish. It's used for fish that cannot handle copper treatments and works with the fish's immune system to overcome the parasite/illness. It does require two or more tanks to be setup, torn down sterilized after each use etc.
Copper QT treatments are good for ICK and Velvet but can also negatively impact the fish's immune system, opening them up for potential bacterial/viral infection soon after introducing them to the display tank. Other parasite QT treatments can consist of Prazi-pro, or antibiotics for other types of issues. At the very least all new fish need to be isolated for at least 7-10 days when you get them home to ensure you don't introduce something like velvet or brook to the tank, and inadvertently kill most if not all your fish.
QT for corals , highly recommended as they can carry a host of other parasites or nuisance algae along with them. Dipping new corals in a commercially available solution or with more advanced methods is at the very least a must do. You'd be amazed at how much can/will come off of a new coral when it goes into be dipped. I have seen bristle worms, flat worms, star fish. zoa spiders, and all sorts of other pests.