When I took the PMP exam, I found it surprisingly difficult, and I found that it took me several months to prepare -- and that was after I had written another book on project management.
Some people have very little trouble with the exam, and don't need much preparation. For example, there are many companies that use most of the PMBOK(r) Guide practices, processes, tools, techniques, inputs, outputs and deliverables on the job. For someone in a company like that, the exam material is very familiar, because they've already encountered everything on the job, so it's basically a multiple-choice exam on their day-to-day work.
On the other hand, there are many people who have only encountered some of the ideas and concepts that they'll see on the exam, but have never come across the others. We wrote Head First PMP with those people in mind, which is why we explained everything in detail without assuming any prior knowledge.
So there's no one answer to how long it will take. I recommend starting in on the material. If you use Head First PMP --and I hope you do! -- then just go through it. Once you're done, take the 200-question final exam to gauge how well prepared you are.
Author of Learning Agile, Beautiful Teams, Head First C#, and Head First PMP (O'Reilly)