If your tank water gets cloudy during this process, don't freak out.
If your tank is cycled properly, you shouldn't be able to detect ammonia or nitrites once it's established. The whole process usually takes 4-8 weeks (I know. I hate it, too) depending on your setup and if you take steps like adding bacteria or old filter media to speed it up. If your tank water gets cloudy during this process, don't freak out. That'll go away on its own as the cycle continues if you don't have too much ammonia.