Yeah, if you see ammonia or nitrItes, do daily water changes to keep them both down. Over a period of the next two weeks or so you'll see your ammonia drop and your nitrite rise. Bacteria slowly grow and eat the ammonia that the fish waste/food produces and process it into nitrite. Then in another 2 weeks or so more bacteria will grow that eat nitrite and make it into nitrate. When that happens your tank is cycled. Nitrate is not very toxic to freshwater fish and they can do ok with levels up to 80ppm (anything 0.25ppm of ammonia or nitrite or higher is bad). You can add some hardy live plants and they'll keep your nitrate levels to almoast nothing, and help keep algae from getting a significant foothold.
I'd actually add some plants right away as they also can use ammonia and help ease the cycling pressures on the tank. Some Anubias, Java Fern, Echinoderous, and Sword species tend to be the hardiest and really only require light and fish waste to survive. The general rule of thumb is the bigger and darker green the leaf, the easier it is to keep. In addition to adding plants, decrease your feeding volume to only what the fish can eat in 1-2 minutes. Slightly hungry fish are better than poisoned fish from rotting food.
Once your bacteria colonies and plants build up over the next month or so you'll have the proper biological filtration to keep ammonia, nitrate, and nitrite at bay, and they wont be much of a problem. In a truly cycled tank, the only time ammonia and nitrite should enter the picture is if lots of new fish are added, a fish dies and rots away, or disease outbreaks.
Whatever you do, dont add more fish until your ammonia and nitrite are back to 0. Keep up with the water changes, dont forget dechlorinator, and good luck keeping the rest alive.