You can fly a plane before you get your drivers license, but  to get your actual private pilot license you will have to wait till you are 17.

To get your private pilot license you must pass a complete a course with aprox. 40 hours of training.  Your training will include a cross country flight of ten hours.  Then you will have to take written exam, and then pass a practical flight test with an examiner. 

 You often hear about young pilots who have their private pilots license before they have their drivers license.   You still have to be 17 to get your pilots license (may be younger in some places) but there is no age limit to practice flying with a certified instuctor (dont quote me on that).  That is why you will hear of young pilots.  Recently in Britain Ed Gardner became the youngest passenger pilot in the country.  He is only 20 years old and flys a Boeing 737 for  Titan Airways.