You'll need to file ATF Form 4 (in duplicate) with a recent photograph attached to each copy. (Passport photos are generally recommended) You also need to submit fingerprint cards with the Form 4, and your Chief Law Enforcement Officer needs to sign his approval on your Form 4. Submit all the paperwork to ATF with $200, and wait for their approval.
25 years ago, approval took about 4-6 weeks. I'm not sure how long it takes these days.
Find a Class 3 dealer in your area. He can help you with all the application details.