Qualifications
As the saying goes: give a person a fish, they will eat for a day, teach a person to fish, and they will smell bad for life. Seriously though, learning to be a fisherman through hands-on experience is the only way to become one. So you go to Fishing University and get your degree in Aquatic Sciences, right? Not really.
While there are fish-related college degrees, they're for people who intend on managing fisheries or working as Fish & Game Wardens. You, the nitty-gritty captain of your own destiny, really just have to set sail and see what happens.
The right fishing professional is the person who either grew up on the sea or really, really wishes they did. We'd say you have to have a strong stomach, but if you can't get over the sea sickness rather quickly, you're not going to last long anyway.
The long hours and weeks/months spent at sea require people with patience, strong will, and absolutely nowhere else to be (source). You'll also need to know a thing or two about mechanics, as a boat adrift without a working engine is not a situation you want to find yourself in. As for the smell, well...eventually you get used to it.