I'll throw in my agreement with the others above. The average we quote a lot is 4 to 6 weeks, even though the truth is that the amount of time it takes a given individual to fishless cycle a filter varies in the extreme.
On the short side there are those who manage to get a contribution of mature filter media material from a mature tank of someone elses and have it work and they only take a week or two. Then there are those that get a mature media contribution but it somehow fails and it still takes them weeks. Then there are the people that are right on the average and see their nitrites finally begin to drop seriously right after the 21 days that is right there in the discussions of average times.
On the other side of this bell curve are people that find they have a problem somewhere along the line. Perhaps they had something wrong with their ammonia and had to start over. Most common of all are those who have problems from very soft water or pH crashes or low pH in general and things stretch out to a couple of months. Enough of all that happening and it can stretch out to 3 months for some, but this is getting on the extreme side.
One nice thing that helps one to be patient is that the process is inevitably going to get there if you just keep testing, putting ammonia in and paying attention. Mostly it just works, if you are patient enough. Its very, very rare that we hear of anyone finding a fatal problem that causes them to start all over.
locust brings up a good point. Be sure to give yourself the best possible start with the right types of filter materials - you don't need carbon and certainly not zeolite or any other chemicals that might mess up the whole process. Coarse sponges, fine sponges, ceramic rings and ceramic pebbles are the most common biofilter media materials currently used.
~~waterdrop~~