-the quarantine tank setup,
-maintenance of the tank,
All three components work together for a successful quarantine experience.
The Quarantine Tank
The quarantine (QT) tank should provide at least 10 gallons of space per fish. Sufficient space is always important for goldfish, but it becomes especially important in quarantine. Quarantine should be a time for new fish to de-stress and get used to their new surroundings, but they can't de-stress if they're crowded. Accumulated toxins from waste will increase their stress, and that's why providing at least 10 gallons of space per fish is so important.
The tank does not have to be a traditional glass aquarium, but it should be a container with clear sides to provide a good view of the fish. It will be important to notice any signs of disease, and that's difficult to do without a clear side view of the fish. Sterilite brand storage bins are always food-safe, and thus are a good option for a QT container. Not all brands of plastic bins are food-safe (and thus, safe for fish) so do your research before buying a container. For larger plastic tubs, it's a good idea to use some sort of brace in the middle to keep them from bowing out too much when filled with water. You can easily make your own brace out of plywood (see photo below).
The next consideration is filtration for the QT tank. It's very important to have at least 10x filtration for sufficient water flow through the filter media. This means that for a 10 gallon tank, you'll need a filter with a flow rate of at least 100 gallons/hour. I prefer to use Aquaclear filters for quarantine tanks because they provide a lot of space for filter media, and they're highly customizable. You can essentially use whatever type of filter media you want in them. The filter should have a thin bottom layer of sponge (cut the large Aquaclear sponges in half lengthwise). On top of the sponge layer, the filter should be filled to the top with biological media (ceramic beads and rings, bioballs, etc.). All of this biological media should be taken from a healthy and well-established (cycled) tank of yours. Ideally you should add the cycled media to the QT filter immediately before adding your new fish to the QT tank. This way the beneficial bacteria living on the filter media won't starve by being placed into a tank with no fish for a few days while you wait for your new fish to arrive.
If you find that the filter output is too strong for your fish, you can cut a long strip of filter floss (a cheaper option is 100% polyester quilt batting) and secure it to the sides of the filter using small clamps (see photo below). This allows you to maintain a high flow rate with your filter while keeping the strong current from pushing your fish all over the tank. For very small or weak fish, it can also be a good idea to cut out a small cube of sponge, cut a hole in the top of it, and place it over the filter intake. This will keep small and/or weak fish from getting stuck onto the filter intake.
Lastly, an air stone is always a good addition to a quarantine tank. It's important for the water to be well-oxygenated to decrease stress on the fish. Don't forget a thermometer too!
The video below shows my QT tank as an example. It's a 27 gallon Sterilite storage bin with an Aquaclear 110 filter, an air stone, a glass thermometer, and a brace (made from a wood clamp) across the middle.
Diligent tank maintenance is always important for goldfish, but especially so during quarantine. Once again, proper tank maintenance will help the new fish de-stress in its new environment rather than adding to its stress. Even though the filter is full of biological media that should be full of beneficial bacteria, you will still need to test the water daily for at least the first week of quarantine. You'll be testing for ammonia, nitrite, nitrate, pH, and checking the temperature. The best test kit to use is the Freshwater Master Test Kit by API; it contains all the tests you'll need at a reasonable price. Ammonia and nitrite should always be zero, while nitrate should be less than 10. The pH should be stable, and somewhere between 7.2 and 8.4 (goldfish tolerate a wide range of pH, as long as it remains stable). If at any time ammonia or nitrites register, a water change should be done immediately. Your test kit and Python water changer will become your best friends during the quarantine process!
It's a great idea to do a near 100% water change for the QT tank every day for the first week or so. Keep in mind that the fish is stressed and very susceptible to disease at this time, and fresh clean water is the best prevention against many goldfish diseases. After the first week, water changes can be gradually scaled back as long as the water parameters remain at acceptable levels. I recommend using Seachem Prime to remove chlorine and chloramines. Prime is very concentrated, so you don't have to use a lot of it, and it's great because it also provides temporary protection in case of a sudden ammonia or nitrite spike. It detoxifies ammonia and nitrite (up to a certain ppm) for up to 24 hours.
Hopefully you had the benefit of seeing your fish (photos, video, or in person) before it arrived so you could be sure to pick a fish that seems healthy. But it's important to remember that even if a fish seems healthy at first glance, it could have issues that may eventually be transferred to your main tank. And that's why quarantine is so important! Typically, it should be assumed that all new goldfish have some type of parasites, and they should be treated accordingly. The most typical medication used on new goldfish arrivals is salt. That's right, just plain old NaCl! It must be pure salt with no additives though, so your average table salt won't cut it. I typically use and recommend API Aquarium Salt, which can be found at most pet or fish stores. The purpose of the salt treatment is to kill an assortment of external parasites, and to do this the salt concentration must be brought up to .3%. .3% is 3 level teaspoons per 1 gallon of water. It's best to bring the salt concentration up slowly to avoid shocking the fish. First add 1 teaspoon per gallon. 12 hours later, add another 1 teaspoon per gallon. Then after another 12 hours, add another 1 teaspoon per gallon of water, and the salt concentration will be at .3%. The salt should always be dissolved in a bucket of tank water before adding it to the QT tank. Never add salt to the tank without dissolving it fully first. Keep in mind that with each water change, you'll need to add back the amount of salt you took out. For example; if you change 90% of the water, you will need to add back in 90% of the salt that was in the tank before the water change. A salt concentration of .3% should be maintained for about three weeks to be sure any possible parasites are killed off. During this time salt creep is a very real danger, so if in doubt, err on the side of caution. As time goes on, it's a good idea to use a little bit less than 1 teaspoon of salt each time you measure, in an effort to offset salt creep.
* You can also use Morton Canning and Pickling salt. This is much cheaper than using API aquarium salt, and it is just as effective and pure. Keep in mind that because the grain size of Morton salt is so much smaller, .1% is 3/4 teaspoon per gallon (instead of 1 teaspoon per gallon).
Prazi is the other medication typically used in quarantine, and this treatment kills gill and skin flukes. Flukes are so common in goldfish that all new fish should be treated as if they have flukes. Prazi is a relatively "safe" medication to use as it's difficult to overdose. The most common type of prazi used by goldfish keepers is a liquid form, called PraziPro. It's not as common to find this in local stores and you may need to order it online, so plan ahead! The prazi treatment must be done in several repeated doses, because it only kills adult flukes, and does not touch fluke eggs. The fluke eggs will not hatch with prazi present in the water, so each dose must have a couple days in-between with no prazi in the water to allow the fluke eggs to hatch so they can be killed. I prefer to keep prazi in the water for 3 days, followed by 2 days with no prazi, and repeat this cycle 4 to 5 times. In a QT tank, you'll be changing the water daily, so the prazi should be added after each water change for three days. For two days after that, do the water changes like normal, but do not add prazi. Then repeat this cycle through 4 or 5 more treatments. The prazi treatment can be done at the same time as the salt treatment.
Here's my video explaining how to dose the Aqua-Prazi:
Some people choose to wait a few days before beginning any salt or prazi treatments. I actually think this is a really good idea, because it gives the fish a chance to settle in and de-stress, and it gives you a chance to observe the fish's behavior before starting treatment. If you're in no rush to get the fish out of QT quickly, then waiting up to 1 week before beginning any treatments may be a good idea. Regardless of when you decide to begin treatments, be sure to carefully observe your new fish for the duration of their quarantine so you can detect potential problems early on.
And last, but not least, enjoy your new fish! If you follow the steps for proper quarantine, it's very likely that you will have a happy and healthy new fish that won't introduce diseases into your main tank!