An aquarium that has not properly cycled will have ammonia spikes, an ammonia is not well tolerated by most aquarium fish. However, goldfish tolerate ammonia fairly well, and sometimes they are put in a new aquarium to speed the cycling process. They do that because they're very messy. When they create all that waste, the bacteria that converts wastes into plant food will become established, thus giving you a cycled aquarium. But now, what do you do with the goldfish? They don't mix well with traditional aquarium fish.
One good way to cycle an aquarium is to add plenty of live plants and put in a small pinch of fish food every few days. Or if you have an already established tank, just borrow some gravel from it. Some people will operate a sponge filter in one aquarium. The filter grows good bacteria, and it can be used to quickly cycle a new aquarium. Just be sure to test the water chemistry, and don't add delicate fish before the tank is completely cycled. After that, do a 10 to 20 percent water change every week.
Please don't hesitate to ask more questions, and I'll try to give less long winded answers.
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