Depending on the state, there's usually a certification prerequisite (i.e., you need to be an EMT-B to become an EMT-B instructor, a Paramedic to teach Paramedic classes, etc.). There's typically a course involved (in Massachusetts it's called "Instructor Coordinator") that includes both classroom and a practical internship of varying length (usually at least an entire EMT class length).
Classroom topics include educational theory, learning styles and motivation (Maslow's theory, Piaget's research, etc.), teaching techniques, state requirements, and written and oral skills.
That's probably the _minimum_ to teach; depending on where you're teaching you may also need a degree (B Ed, M Ed, etc.), experience, and associated certification (NFPA 1041, BLS / ACLS / PALS instructor, etc.).
It can be rewarding as a career, but it can also be difficult on many levels - you need to balance student needs, administrative demands, state and other oversight, and time scheduling. Depending on the group dynamic you may find yourself trying to get a group of students up to speed with basic math skills so you can teach Math for Meds or playing negotiator between several different groups of students just so you can get on with your class. So outside of the regular requirements you'll probably need a great deal of patience and empathy as well as some good negotiation / political skills.
