You start out by challenging your cycle, this means that you have some source of ammonia. This can come from something as simple as flake food, a fish, a dead shrimp, adding new live rock to the tank.
This ammonia then is converted to nitrItes, and then to nitrates. When complete the cycle should bea bout 6 weeks long +/-. The longest is the nitrAte phase that takes about 3 weeks itself.
In the end you should have 0 ammonia, 0 nitrItes, these are the most toxic. You should then be left with low nitrAtes and you should have a means by which to assist in removing nitrates. This can be done with simple water changes.
The nitrAtes are not as evil as many folks think, they do not have to read "0" on the test kits. They should be below 20 in my opinion with 10 being better and you can always strive for zero, but many corals actually use some nitrates so there should always be some in the system.
Thomas