Qualifications
Well, you'll need a farm. Forty acres of fertile dirt. One mule. You don't technically need a degree to be a crop farmer, but the industry is becoming more and more picky and sophisticated (source). So unless you just want to be a farm hand, always heppin' and shleppin' for The Man, it's important to have an advanced degree.
Proficiency in math, biology, chemistry, and other life sciences is becoming increasingly essential when it comes to such matters as understanding what provides for ideal growth and how to maximize your yield, compete with those Chileans...or to at least be seedy. (Sorry.)
You also need to be very business-savvy. Make the wrong deal with a buyer, and you're dead (financially). Buy too much—or not enough—seed? Dead. Missed that boll weevil bug? Dead. Niedermeyer? Dead. Smart business dealin' is a must. And that's not something that happens by just sitting around picking potatoes.