Adding fish to an uncycled aquarium is like breathing in toxic chemicals.. which is why it is Essential that every aquarist understand how the nitrogen cycle works.
When fish poop or un-eaten food breaks down in your tank it produces a chemical called Ammonia (NH3). As you build your bennefical bacteria culture in your tank a new bacteria called Nitrosomonas. This bacteria will break down the ammonium (NH4) or ammonia (NH3) and turn it into Nitrite (No2).
We now rid one toxic chemical and gained a new one…. The next phase in the beneficial bacteria cycle is a strain called Nitrospira. This bacteria will break down the Nitrite (NO2) and turn it into Nitrate (NH3).
Nitrate is not toxic to fish or corals at low levels. You should aim for a level of 10ppm or less however many aquarists have no issues at levles in the 15-30 range.
When cycling a tank you will want to test every few days to monitor where your aquarium is in the cycle. To kick off the process you will want to use an ammonia source to feed the tank. This can be done using fish food, a raw shrimp or my preferred method of using bottled instant cycle bacteria such as DR Tims one and only then using fish or 100% pure ammonia. (ONLY add live fish IF you are using a live bacteria instant cycle product)
At first 
you will see your ammonia rise then start to drop. as your ammonia starts to drop you should see your nitrites start to rise then fall, when the nitrates rise the ammonia and nitrite should start to read 0 or close to it. This process can take 5-6 weeks if you using dry rock/sand. 1-2 weeks or less using live rocks and 1-2 days if using a product like DR Tims one and only.
Now we got rid of Ammonia and Nitrates.. but we are left with Nitrate? yes, yes you are! The simplest way to lower you nitrate is through your regular water changes.
The other way to lower your nitrates is through growing and harvesting macro algae such as chaetomporpha or dosing a carbon source such as vodka.