Assuming your in VA, it is a CHP. The process if fairly simple.
Here is the application form is PDF that you can fill out and print:
You then submit this form to the circuit court (sometimes the police dept, depending on which city/county you live in). Look at your local government's website to see exactly where to submit your application.
The court has 45 days to approve your application is issue the permit or tell you why not. VA is shall issue. You don't have to provide your SSN.