We are forgetting nitrate in this equation? When ammonia and nitrite are 0, the nitrate is not necessarily low enough to begin stocking.
Before you begin stocking with living animals, ammonia has to be 0, nitrite has to be 0 and nitrate should be around 20.
The last thing to spike will be the nitrate and you will have to do some small water changes, 15 or 20%, until the nitrates are down.
As Barry has said, search the threads for cycling. Better yet, get a book that describes the nitrogen cycle and how it relates to aquariums. Your experience with this hobby will be better if you have a good understanding of the cycle.
There can't really be a good answer to the question "How long does it take", but a few weeks to over a month, generally speaking, and depending on many different factors.