Basically, ammonia levels rise, drop, nitrite levels rise, drop, and nitrate is there.
Thats basically a rough idea of what happens, but all three, ammonia, nitrite and nitrate are chemicals(i think thats the word) which will kill your fish.
I believe one of the main reasons you do water changes is to keep your nitrate level down
To make your tank cycle, put used filter media in your filter, used gravel, and a couple of "hardy" fish.
You dont have to put used filter media and gravel in your tank, that just makes the cycle go from 3-4weeks to a few days or a week.
Edit: Oh yeh almost forgot, if you want to "Fishless Cycle" you'll need some pure ammonia or w/e its called.