What you are trying to create in your tank is a colony of beneficial bacteria that can process the fish's waste (ammonia) into a less toxic substance, nitrate. The "cycle" that is spoken of, is the fish's ammonia being processed into nitrite by one type of bacteria, this nitrite being processed into nitrate by the second type of bacteria, and this final product (the nitrate) is removed either by you during a water change or by real live plants using the nitrate as a fertilizer to grow.
YOu cannot get the beneficial bacteria to grow in your tank if you do not feed them. They need ammonia to grow. Unless you can find a source of bacteria to seed your tank with, you need to grow your own. This takes time - but will happen. By adding a source of ammonia to a tank and waiting, the bacteria will colonate and begin to grow.
The first type of bacteria will appear when there is ammonia to "feed" on. WHen they produce quantities of nitrite, the second type of bacteria will then appear to "feed" on the nitrite producing nitrate.
Your source of ammonia to start this cycle can be pure ammonia from a bottle (fishless cycle) or fish waste from some "sacrificial" fish - hearty fish that stand a good chance of surving the stresses of a cycling tank.
Your tank will never cycle just by sitting there. You need to add a source of ammonia. By putting your tetras into the tank, you will start the ball rolling.
ADd your tetras and test your water for ammonia the first days. You will probably see some ammonia. Since you have a 20 gallon tank ( Did I remember right?), two tiny tetras will not produce too much waste. You will only get a small ammonia reading. You should be fine for quite a few days. You will want to try to keep the ammonia at around 1ppm give or take some. When you see the ammonia reading starting to drop, and/or after about 1-2 weeks, test for nitrites. If you see some nitrites appear, you have completed the first step of cycling. Nitrites are a little nastier than ammonia to the fish. You want to try to keep them around 1-2 ppm. too. There are some tricks to helping the fish through nitrite spikes - salt and such. We can walk you through that when the time comes. Finally, after your ammonia drops to zero, and the nitrites appear to be diminishing, test for nitrate. If you see the nitrate reading rise, then you are almost completely cycled.
Several comments, though. With such tiny fish in a relatively large tank, you may never see much spiking of the various components of the nitrogen cycle. It may happen rather gradually. This is not all bad - it certainly is nice for the tetras!
You also need to realize that the cycle that is built from two tiny tetras will not support the waste of a messy goldfish. When you add a goldfish, the cycle will take a day or two and "bump" - show ammonia or nitrite - but should rapidly grow to the size needed to process a goldie's waste. Add one goldfish at a time.....and give it a chance to grow into it. A few days between fish is a good idea. Test the water and you will be able to tell how it is growing.
I expect you already read these articles on cycling, but I will post the links just in case you have not seen them yet.
Please feel free to ask any questions you may have. Sometimes it is hard to type what I am thinking and it comes out all jumbled up and not too clear. I apologize - I am having a "senior" type night tonight!
http://www.kokosgoldfish.com/cycle.htmlhttp://www.kokosgoldfish.com/FishlessCycle.html