Creating a mod team or starting out in another position in the gaming industry are both very good ways to get your foot in the door. As for schooling, management and things of that nature are good things to study. Like Joe said earlier, some of the best producers started out in other positions and moved their way up. Starting from the bottom and being involved in different areas of the development process really gives you a grasp of what is involved in making a game. It really opens your eyes to things you just wouldn't know if you, say, only knew art or only knew design. A good producer knows a couple of the different departments, while a great producer knows everything!
Being very outgoing and understanding also makes for a great producer, in addition to having good problem-solving skills. It's hard to find people that are good at all of these things, and i'm pretty privileged to be working with some of the best.