In a healthy, enclosed system (e.g. a fish tank) the nitrogen cycle is a continuous process that converts ammonia to nitrite, then to nitrate, and then into nitrogen gas.
This guide explains the workings of the nitrogen cycle in aquariums and how to monitor accumulations on biofilter media if you're setting up your first tank.
In the beginning, nature creates food (e.g. microorganisms and plants) and then fish eat food and produce waste.
Nature also breaks down the fish waste and it gets converted into food again.
But, the part of the nitrogen cycle that applies most for aquarium hobbyists is where the waste products from fish turn into toxic nitrogen compounds, such as ammonia, nitrites, and nitrates.
In fact, these nitrogen compounds are capable of killing your fish. That's why you also need to have a good supply of beneficial bacteria and plants to consume the waste products.
Here's a simplistic chart that shows the basic steps of how the aquarium nitrogen cycle works:
Pro Tip: It's reasonable to expect the amount of nitrates to build up over time and be potentially harmful to your fish. So, you need to remove high levels of nitrates. You can lower nitrate concentrations by changing the water on a regular basis or by allowing "living" aquarium plants to consume the nitrates as they produce new leaves.
In simple terms, "cycling an aquarium" is the process of having sufficient biological filtration. Thus, having plentiful beneficial bacteria or growing plants means the ammonia and nitrites are getting consumed before the levels reach dangerous concentrations.
You can use ammonia test strips and multi-test strips to monitor the levels in the tank water. A good reading would be zero (0) ppm ammonia, zero (0) ppm nitrites, and a small amount of nitrates
But, you should change some of the dirty tank water for fresh, clean water if the nitrate concentrations reach forty (40) ppm or higher.
In general, you should wait for two (2) to six (6) weeks for a fish tank to cycle. But, it can take several months if the quality of the water is low.
Here's the thing:
Introducing some "live nitrifying bacteria" is going to help you speed up the aquarium cycling process. You might also have access to some used filter media (e.g. from the stockist), or you can start growing live plants (they will contain some beneficial bacteria).
In a nutshell, it's not easy to know when the aquarium is "cycled". But, you should be able to confirm whether the level of beneficial bacteria is enough to treat the waste produced by the fish.
So, how will you know when there is enough biological filtration inside your aquarium to handle high levels of toxic nitrogen compounds?
One of the easiest and cheapest ways to improve biological filtration in your tank is to add more aquarium plants (not plastic). More growing plants will be consuming more ammonia and nitrates produced in fish waste.
A note of caution! Remember, adding more plants means they'll need to feed on lots of fish waste. So, if you have too many plants and not enough waste-producing fish, the plants may starve and die. Even so, using an all-in-one fertiliser (e.g. Easy Green) is a good way to counteract this issue.
Some beginners wrongly assume that having several big filters inside one tank is going to increase the amount of bacteria. In fact, bacteria does grow on filters, but it also grows on every other surface in the aquarium, including the glass walls, plastic ornaments, and the substrate (gravel).
It's also true to say that you may have greater capacity to support more beneficial bacteria if you have more than one filter. However, the decorations alone may provide you with enough surface area to colonise beneficial bacteria if you only have a few fishes.
Pro Tip: The main fish keeping hobby section contains more information about setting up a simple home aquarium and why it doesn't need to be expensive.