So you have been reading around different sites, and talking to that kid at the pet store and everyone is talking about this "Cycle". Well what the heck is it? And what does it mean to me? Here I will attempt as easily as possible to answers those questions.
This "Cycle" can be explained as follows:
The drawbacks of biological filtration are mostly associated with startup. What is popularly known as new tank syndrome or The Cycle , there is a lag between the time the fish are placed in the tank and the time the populations of bacteria are large enough to process the ammonia and nitrite.
When a tank is new, it has nothing in it (except for water, etc.) but nothing biological (living organisms). Now you add fish, these fish eat, and thusly they produce fecal matter (fish poop) as well as urinary waste. Any excess food and nearly all the fecal matter will fall to the bottom of the tank and into the substrate. Once there, this matter begins to break down. The first thing is that a bacteria field begins to grow and feed off of this matter. This bacterium breaks down the matter into toxic ammonia (NH3). Ammonia is quiet deadly to fish (I don't like it much either myself). In new tanks, there simply isn't enough bacteria growing yet to break down everything that is thrown at it, as quickly as it needs to. One way of speeding this process up a bit, is by adding commercially grown a bacteria culture, generally available at your local pet stores. I do not recommend this course of action for beginners, but with a bit of experience behind you, this can be a rather effective way of jump starting an aquarium before actually adding fish. One word of caution here, many of these products ask you to add the bacteria weekly. Once you have your fish in the tank, stop using this product, all you are doing is lining the pockets of the retailer and manufacture, your fish will provide enough matter for your existing bacteria field to thrive. This is known as the first 3rd. of the "Cycle".
The second 3rd, of this "Cycle" is that as the bacteria grows it feeds not only off of the excess waste, but the toxic ammonia (NH3) as well. This toxic ammonia (NH3) is converted to another toxic compound called nitrite (NO2) by the Nitrosomonas species of bacteria. Nitrites are also quiet deadly to fish, even in small amounts.
The third portion of this "Cycle" is when the bacteria continues to break down this nitrite (NO2) into relatively harmless nitrate (NO3) by the Nitrobacteria species of bacteria. This process is known as Nitrification . Nitrate is removed from the tank through small frequent water changes.
So if you were to look at the graph, you would start at day 0, then as you added fish, a curve would start to grow upwards. The more fish and/or waste food you have the taller the curve. As time goes on, this curve tapers off and begins to fall. This is the 1st portion of the "Cycle (Ammonia). At the same time this curve starts to fall the next curve (Nitrites this time) begins to climb. This may also go as high as the first curve did. Now the first curve is tapering off near the bottom of our graph, the second curve is beginning to crest and head back downwards a third curve starts upward, but not to the extent the first too did, this is the harmless Nitrates.

So this graph is over a period of 30-40 days, the first 10-15 your tank can be deadly with Ammonia, the bacteria grows, breaks down the Ammonia, bringing the deadly levels down, but the Nitrites now climb and can become deadly, this is the second 10-15 days. And the last 10-15 days the Nitrites and Ammonia has settled down and the Nitrates are on the rise.
This is why I stress throughout my site that for new tanks, go very sparingly on adding fish, usually no more than 1-2 inches of fish added per ten gallons of water for the first 15 days. These fish (commonly called "starters") start the whole cycling process. Afterwards when things calm down in the water, you do not want to add anymore than 3 fish in any 7-day period of time to avoid these problems repeating themselves. When this happens it is commonly called "Spikes" or "Spiking". The sudden heavy increase in fecal matter, the bacteria field that breaks this fecal matter down is not large enough to combat the sudden increased load, thus ammonia shoots up for a period of several days, then the Nitrites will soon follow.
Red gills, fins or under bellies you see is generally due to excess Nitrites, a water change of 20-25% is in order, and again in 48 hours. Another great way of dealing with excessive nitrites/nitrates is to add absorption pillows to the tank. These pillows are relatively inexpensive and best of all, reusable. Nitro-Sorb is the brand most popular in the U.S. Try not to disturb the gravel at all, especially do not try to "clean" the gravel. If the fish survive the next week or so, you should have smooth sailing after that. I know its tough not to suddenly stock a tank full of fish, but one thing this hobby teaches us, patience, patience, patience.
