You normally use a smaller tank that holds about 20-40litres of water. the tank has little if anything in it. The less shell, sand, etc in the tank the less stuff there is to encourage bad bacteria to develop and the easier it is to treat the tank should the fish become sick. For marine fishes it is a good idea to have a thin layer (less than 1/4inch or 5-6mm) of sand on the bottom. You can use some plastic plants for ornaments and to give the fish security. It is a good idea to have a heater and established filter in the quarantine tank. A spare filter can be run in the main tank until it is needed for the quarantine (Q) tank.
The fish should spend at least 1 week but preferably 3-4 weeks in the Q tank. During this time it is fed and looked after just as it would be in the main tank. However, if it develops a disease then you treat it in the Q tank and the disease does not get into the main tank. If the fish is treated for a disease then the quarantine period starts again after the fish has recovered from the ailment. Basically if it gets sick it spends a couple more weeks in the Q tank after it is better.
When the fish has been in the Q tank for a while and has shown no signs of disease, it can be added to the main tank where it will spend the rest of its life.
The Q tank is then washed out and disinfected. If it is a saltwater Q tank then you can fill it up with freshwater for a few days before rinsing out with freshwater and allowing it to dry. This will kill most things. The filter can be washed out in freshwater and put back in the main tank.