Find out what the requirements for investigators are in your area by contacting the district attorney's office. Generally speaking, you will need to have completed at least 2 years of college (some require 4 years) in police science, criminology, criminal justice or some form of public administration; three years' experience as a peace officer (including investigation duties), U.S. citizenship and a valid driver's license. Many district attorneys will accept other experience that can be substituted, such as experience as a private investigator in exchange for experience as a police detective.
Apply for the position. Even if there are no jobs available or the position doesn't exist, make yourself known as a candidate and get a copy of your resume and business card to the district attorney's office. You may be able to apply to more than one district attorney, depending on whether you have to be a local resident.
Follow your application's progress. If they have a shelf life of six months with the district attorney, then make sure that you re-apply after that period. Keep track of changes in the DA's budget to see if more positions will be added, and keep an eye on which investigators are leaving to see if there's an opening you can fill.