I totally agree with what Brenden says. I think in my first response, I said Nitrates...I meant Nitrites. As ammonia spikes, nitrites will start to rise. At the same time, you should see your Ammonia levels fall. Your Ammonia levels need to reach 0. As your Nitrites spike, you'll start to see Nitrates rise. Your Nitrite levels need to reach 0. This indicates that your bacterial colony is becoming established. Your Nitrates won't fall on their own really. That's where exporting Nitrates comes in. To start with, the best way for you to do this will be water changes, using RO/DI water, unless you have exceptional water out of your tap. Eventually, you can also help export Nitrates using Macro Algaes along with water changes.
Keep in mind that even when your levels end up where you want them...that only indicates that your biological filtration is adequate for the waste you have in the tank at that time. When you add fish, you'll need to allow time for the biological filter to grow to accommodate more waste, more bio-load. To start out, when you add fish, you'll probably notice a slight rise in Ammonia, then Nitrites. Ammonia and Nitrites are both lethal to fish and inverts. Fish will be able to tolerate a slight level of Nitrates but, as Brenden stated, you'll want to wait to add corals or other inverts until your Nitrate levels are at or very near 0. You may need to add a small clean up crew in the near future though. Other's will probably chime in with suggestions also.