Here is a guide for the aquarium cycle, and various ways to go about it including the use of pure ammonia:
If you buy ammonia in a store, it will most likely be labeled as Ammonium Hydroxide (NH4OH). Plants, and bacteria, do not care what form the ammonia is in and will use it all the same (plants actually will convert ammonia to ammonium before using it as a nutrient). You will need to ensure the ammonia you buy has no additives of any kind (scents, surfactants, dye, etc).
The test kits that we use simply look for NH3, regardless of what form it is in. That is why, even when using a conditioner that detoxifies ammonia (Prime for example) your test kit will still show the presence of ammonia ... because it is still there.
These water conditioners have an effective period, I believe with Prime that is 48 hours. In a cycled aquarium that is plenty of time for the bacteria to process the ammonia found in tap water and convert it to Nitrite, and then Nitrate.
Ammonia will not 'evaporate' or otherwise out gas from water left sitting for a day. I believe you are thinking about chlorine, which exists in water as a dissolved gas and will escape the water either over time or with aggressive agitation. This does not work with Chloramine (NH2Cl) which many municipalities are switching to for treating drinking water which is why it is important to use a water conditioner that works on both Chlorine and Chloramine.