No government agency -- federal, state or local -- regulates CPR the way they regulate paramedic or nurse licenses. CPR is a skill rather than a license to perform patient care. Anybody can get certified and anybody can do CPR whether certified or not.
There are hundreds of organizations and businesses offering CPR certifications. Whether or not a particular certification is honored depends on who's asking. Within the healthcare field, only the American Heart Association's CPR certification is universally accepted by hospitals and EMS agencies. The American Red Cross's CPR certification comes in at a close second.
The only other organization I would consider using is the National Safety Council. There are lots of online CPR organizations that gladly take your money in exchange for a card, suitable for your wallet, which proclaims your proficiency in CPR. Online CPR certifications are bogus; stay away from them.
Becoming an instructor with the American Heart Association (AHA), the American Red Cross (ARC) or the National Safety Council (NSC) is a little different depending on which organization you choose, but it always starts with becoming certified in all of the classes you will be certified to teach.
For example, AHA CPR instructors can teach adult, child and infant CPR as well as Healthcare Provider CPR, which includes the other three levels. In order to become a CPR instructor for AHA, instructor candidates have to be certified in Healthcare Provider CPR from AHA before taking the instructor courses. ARC and NSC have similar requirements for their instructor candidates, but since there isn't any oversight, each organization names their courses differently. What is known as Healthcare Provider from AHA is called Professional Rescuer by ARC.
Once you become certified at the level necessary, you must register for an instructor course. The American Heart Association uses a core instructor class, which covers adult learning concepts and basic teaching methods. In addition, instructors have to take a course to learn how to teach CPR specifically (AHA has several course offerings that all use the core instructor program in addition to individualized instructor training).
Once you become a CPR instructor, the organization with which you are affiliated will sell you the materials necessary to teach classes. The process is a little complicated and can take a while, but it is quite worth it if you want to become a CPR instructor who is respected and reputable.