Find out who the issuing authority is. This is the agency to whom you will submit your carry and conceal weapon application. Your state's government website will have this information.
Take a firearms safety course, if needed, and find out the minimum age requirement for your state.
Write a letter justifying your need if you are applying in a "may issue" state. Some "may issue" states are nearly "shall issue" and require no more than a generic statement. Others require employment as a security guard or a verifiable threat on your life.
Fill out an application and pay the required fees. Many states have an online application and almost every state has an application form you can download and print. Every state requires some sort of criminal background check and most require fingerprints and photos, which usually require additional fees. A photo ID is also usually required.
Qualify as a resident, if possible. The requirements and fees are usually lower for residents.
Renew your permit before it expires. Most states just require a renewal fee, but some require you to retake a gun safety course. Some states also allow a grace period on the expiration date.