Break-in period:

When you have just started a biosphere it takes time to perform, unfortunately. Water placed in a new aquarium will be changed quite radically. It takes time for the aquarium to balance, to be able to remove all of the waste material (ammonia) to a less toxic substance (Nitrate). New aquariums generally take about 5 - 7 weeks to able to sustain a full biological load. Thats why you shouldn't just shout "Weeehay!" and chuck in tons of fish at once, it should be a gradual change.

The Nitrogen Cycle itself:

Fish go to the toilet, well, they don't really give a damn they just drop it anywhere, so because of that they add a lot of Ammonia. Its not just fish excrement, its fish respiration, excess food, plant remnants and even any dead fish that cannot be found. If you had a huge amount of water, the ammonia would dissipate quite well, but where you have a new aquarium ammonia tends to concentrate. This is a vulnerable time as no fish will enjoy such high levels, but some are tough (platys, barbs) and can withstand these levels. But your ammonia level is just a stage, as biological filtration and beneficial bacteria will reduce it, but it takes time to do this.

To remove ammonia altogether would be bloody hard: instead, we use numerous bacteria that uses ammonia as a food source. The bacteria strain that is important is Nirosomonas. This strain needs time to colonise the aquarium, the desired population doesn't just happen overnight. This is useful as it absorbs ammonia, and reduce it to Nitrite.

Once Nirosomonas have reduced ammonia to nitrite, beneficial bacterias isn't finished yet. Nitrite can be reduced further to Nitrate. The next step is the bacteria strain of Nitrobacter. Nitrobacter takes even more time to adsorb nitrite, and in this stage nitrite is prominent and it is another dangerous time for a fish, even a hardy one. But, after a while, nitrite levels have reduced and the less toxic compound nitrate is left. Although this toxin is far less dangerous than the earlier two, you must not let it build up in your anquarium. Standard water changes are a chore, but I would recommend you to do them as this reduces nitrate concentrations, and your fish will then be more healthy and will appreciate you for it!! (Well, maybe not but it can prolong the life of your fish). In technical terms, the Nitrogen Cycle process is called Nitrification - the oxidation of nitrogen by bacteria.

This diagram shows the basic Nitrogen cycle in a tropical freshwater aquarium.

This graph shows how the ammonia concentration builds to a spike, then rapidly falls. That is because Nitrosomonas has taken hold, and reduces ammonia to Nitrite. Then Nitrobacter comes along and reduces it further to Nitrate.

 

Also there is always the option of the Fishless cycle which will then prevent any fish going through the hazadous experience.