It might take you a minimum time of three years to become a private investigator, but this will greatly depend on which specialty you select. Basically, there are no official education requirements for becoming a private investigator and you can find out more details on http://www.ehow.com/how_4780639_become-private-detective.html.
Generally, if you go work for a PI agency, they prefer experience in law enforcement or investigation work. It's a catch-22. You need experience for the job but you can't get experience because no one will hire you because you have no experience.