Fish produce ammonia as waste, just as humans produce urea in their urine. Ammonia is toxic to living things and if allowed to build up it will kill your fish, slowly and painfully.
In a cycled tank there is a healthy population of bacteria who convert this ammonia into less toxic forms, first nitrite and then nitrate. The nitrate is removed from your tank through regular water changes. Your tank does not have these nice bacteria so the fish are essentially living in their own toilet.
Fishless cycling means that you add ammonia to your tank before adding fish, to simulate the fishy waste products and encourage the good nitrifying bacteria to grow. The link that Kieran provided explains how to do this. Unfortunately you already have fish so you're now in a fish-in cycle instead.
A fish-in cycle means that you will need to do very frequent water changes to remove the toxic waste products from the tank yourself, until the bacteria are able to take over the job.
You should start with a large water change right away of about 75%.
After that I recommend you do 50% water changes every day. Try to get yourself a liquid testing kit for ammonia so that you can tell how safe the water is. When nitrite starts to appear you can add a little salt to the aquarium to help the fish cope with nitrite toxicity.
Can you confirm that you are using a dechlorinator or water conditioner on water before you add it to the tank?
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