Since your fish must live in the tank all the time, the most important factor for you goldfish is the water quality.
Let's start with the setting up and cycling of the tank.
"Cycling" is the formation of a nitrifying bacterial colony in your aquarium.
Others cycle with fish, I recommend a fishless cycle.
Here are the instructions for a fishless cycle:
1. Set-up your tank
2. Set-up your filters
3. Add some form of beneficial bacteria. This can be Bio-Spira from Marineland, Cycle from Hagen, "live" filter media, "live" gravel, or even water from an already cycled tank. (Your local fish store may even be able to provide you with some live gravel for free, even some old tank water).
4. On the first day, add small amounts of pure ammonia (you'll know if it's pure, there will be no foam or suds if you shake the bottle), testing after each addition until you have reached a level of 5ppm
5. Each day, add that same amount to the tank to help the beneficial bacteria live and multiply.
Ammonia levels will peak and when the bacteria colony is established, it will begin to reproduce. At this point, the second beneficial bacteria colony will begin to grow. This will result in Nitrite levels in you tank rising
Check ammonia levels. When ammonia has peaked and is beginning to lower, reduce the amount of ammonia added by half per per day. Test ammonia and nitrites daily. Nitrites will spike and then begin to come down. When nitrites are 0ppm (zero), stop adding ammonia. The next day do a 50% water change.
The tank is now cycled and you may add your fish. Keep in mind that this process can take anywhere from 2 to 6 weeks. The cycling time will be a little shorter if you were able to "seed" the new tank with some bacteria from an existing healthy aquarium by adding filter media, gravel or even water from an old healthy tank to the new one at the beginning of the cycle, or if you buy some Bio-Spira or Cycle.
Next is regular testing of your water parameters. As with all fish tanks, ammonia, nitrite and chlorine should be at 0ppm (zero). PH should be between 6.4 to 8.3 depending on what type of fish you are keeping. Just ask your LFS or consult one of the many fish websites on the internet.
A filter works 24 hours a day and purifies the water in your tank by removing harmful chemicals and debris. Modern advances have also made filters easier to maintain than ever before. I suggest having 2 filters. By having 2 filters set-up on your tank, you have a back-up in case one should fail and you also have 2 times the filtration all the time.
Finally, the most important thing to know about is the water change. The water in your tank must be kept clean, dirty water can make you fish sick or even kill them. The advanced fishkeeper knows that chemicals like ammonia can build up unnoticed. All you need to know to start is that a regular water change goes a long way toward preventing these kinds of problems. A 20% - 40% water change every week is very important, because of the large amount of waste they produce and the oxygen they use.
Usually, it is ok to use water right out of the tap. Let your faucet run for about a minute before taking any water, then add water detoxifier such as AmQuel Plus, Prime, Bio-Safe, etc before adding to your tank.
Following these simple steps will result in happy fish.