Most cab companies are looking for drivers who have a high school diploma, driver's license, and a commercial driver's license (source). They need drivers who are reliable, level-headed, and have good people skills. No one wants to hire (let alone be in a taxi with) a hotheaded driver who doesn't know how to control their own emotions, much less the steering wheel.
Some cities have taxi cab commissions that set rates and requirements for drivers. These requirements may include an English proficiency test, eighty hours of classroom instruction, a driving test, and an exam.
Training may also be required, depending on the cab company and state. The training usually covers geography, mechanics of the meter, best places to pick up passengers, and how to complete paperwork. And you thought you'd get out of writing forever once high school was over.
Training might also cover the best places to hang your fuzzy dice and pine tree-shaped air freshener, but as a cabbie we expect you'll figure that part out on your own.