For most animals, a 10 gallon glass tank with a small powerhead will suffice. You will need a bacterial culture and the easiest way to do that is to use
sponge filters (that fit on a bubbler.) You can condition the sponge filters in the sump of your main tank and then take them out as needed for the QT. Be sure to clean them well in FW and vinegar before putting them back in the main tank and if you've had to use meds in the QT, it's best to just throw the used sponge away.
You can also use rubble or ugly rock from your sump in your QT but if you have to treat with meds, you won't be able to put it back in your main tank. Also, the porous rock will effect med levels.
If it's just fish, shrimp, crabs etc that are in the QT, you don't need to worry about lighting. If you're QT'ing corals, then you'll need appropriate lighting. You'll need a heater and a thermometer, test kits and to do water changes on a fairly frequent basis, depending on the animal in the tank.
Larger fish may require a larger tank or even a rubbermaid tub as a QT to keep from getting stressed. Non-porous SW safe items (large pieces of PVC pipe work well) for fish to hide in also help their stress level.
Ideally, everything that goes in your tank should be quarantined at least two weeks, some people say it should be 4-6 weeks.
HTH,
Alice