Qualifications
It all starts with being a good pilot and logging a ton of hours for yourself. That is, you start with your own VFR then IFR licenses on a single engine piston/propeller plane. Then you get your multi-engine licenses in both (source).
You might stop right there and "just" be a CFI training student in those classes of airplanes. It's a decent gig that has lots of students (beginners) and carries a lot of freedom. Single engine trainers are more or less where everyone starts, so the base of the pyramid is fat and wide.
In each category, there's a separate incremental license for actually being a CFI—in large part, that license is more or less the same as the one you'll have taken to become licensed as a pilot, only the tolerances are tighter. If you're "just" a pilot, you can get 72% or better on a given VFR exam—for a CFI, you need to have 80% or better. Or retake the exam. Same deal with the flying test itself.
If you move up the food chain, you'll need to get "time and typed"—that is, you'll have to put in a minimum number of hours flying and then get an insurance company to cover you in a given type of airplane. Planes have "classes," which are uber-important, mainly for the kindly, loving insurance people who will have to believe in you—i.e., believe that you won't aieee, splat on them. They're the ones left holding the bill if you do.
Some examples of plane classes are:
- Single-engine piston
- Multi-engine piston
- VLI (very light jet); just one pilot can fly it
- Jet; sometimes one pilot, but usually two
And then there's a "heavy" (i.e., 150,000 pounds or more) and other weight and distance and structural classes. Each carries its own type rating, as far as insurance companies go. As you get higher on the food chain, the insurance world will focus a tighter scrutiny on your abilities than just about any other element in the ecosystem.