The cycle starts with Ammonia (toxic), coming from the fish, fish food and some is found in your tap. Then the beneficial bacteria works to turn the ammonia into Nitrites (very toxic) and finally the Nitrites are turned into the less harmful Nitrates. When you have 0 ammonia and 0 nitrites only nitrates should be present, which need to be removed (with weekly water changes). Nitrates should never go above 40ppm.
If you have your tank set up for over a month, it is probably fully cycled or close to fully cycled, but testing the water parameters is the only way to find out.