Draw from your background. I’m a psychologist by training. Most of the questions that intrigue me center around “Why did he do that?” That’s what I’ve been trained to look for in life. You may think that your chosen field has nothing to do with baseball, but you’re wrong. Sure, there are a lot of guys who are physics/math majors who look at algorithims for figuring out what a player will do next year, and that’s fine. I’m personally waiting for a good Sabermetric sociologist to come along to figure out why it is that baseball teams and society in general are so poor in assigning value to baseball players.
I found that one particularly interesting, especially because I've had a passing interest in sports psychology and mental optimization ever since reading The Mental Game of Baseball. In a world where some statheads mock the notion that professional ballplayers can get nervous or lose focus, it's nice to see one of the premier sabermetricians in the blogosphere single out the mental side of things.
So what am I doing to become a sabermetrician? My master's program had quite a few stats classes, and I consider that a very lucky break since I didn't have any statistics background before that (save "Intro to Probability"). I also just ordered and received Baseball Hacks on Amazon, as well as Learn VB .NET Through Game Programming and the Visual Basic .NET Codemaster's Library. The latter two books were written by Cleveland Indians Manager of System Development Matt Tagliaferri, which is a not-so-coincidental reason why I purchased them.