Anything that breaks down in water will produce ammonia. Fish food, fish waste, dead fish, rotting plant leaves all create ammonia. In an aquarium with an established (cycled) filter, there are good bacteria that eat the ammonia and convert it into nitrite. There are more good bacteria that eat the nitrite and convert it into nitrate. These bacteria will normally keep the ammonia and nitrite levels on 0.
Any ammonia or nitrite will stress fish and high levels can definitely kill fish, so a good established filter is essential to keep the ammonia & nitrite at 0. The ammonia and nitrite damage the fish's gills and internal organs. They have more trouble breathing and can suffer organ failure.
The easiest way to reduce ammonia & nitrite levels in a tank is to do a big (75%) water change and gravel clean the substrate to remove any left over food or fish poop. I recommend doing a 75% water change and gravel clean each day until the ammonia & nitrite are back to 0.
You can do a 90% water change every day as long as the new water is free of chlorine/ chloramine and has a similar temperature and water chemistry to the tank water. Fish are fine with clean water and daily water changes, but they will not tolerate ammonia, nitrite or high levels of nitrate, and they won't live in chlorinated water. So big water changes are fine, just make sure you use a dechlorinator in any new water before it gets added to the tank. The best way to do this is to fill a "Fish Only" bucket with tapwater, add dechlorinator and aerate for 30minutes or so. Then add that water to the tank. You can add a bit of hot water to the bucket to raise the temperature if necessary.
It's also a good idea to reduce feeding to once every second day, and only give the fish as much as they can eat in about 20-30 seconds. Remove any uneaten food after that. The more food going into the tank, the more ammonia that is produced and the higher the levels get to. The same with nitrite. Don't worry about the fish starving, they will not starve. Unlike mammals that use most of the food we eat to stay warm, fish take their body temperature from the surrounding environment (the water). This means any food they eat is used for growing and moving about the tank. Because of this, fish can go for weeks or even months without food and still not starve.
