I had a couple of guys from another forum that basically introduced me to it slowly.
I never read any books at the time or anything, there were just basic baseball discussions going on, and they constantly won those arguments because of their knowledge on the subject.
I first came to more saber-minded statistics in the beginning of the off-season of 2006 when people online were saying how Ryan Howard should be the MVP. Being a Cardinal fan, I felt Pujols was the better player, but I didn't know how to prove it....and I was being a homer (admittedly) at the time. I wanted Pujols to win the MVP because I was being a fan.
My two 'online friends' quietly agreed with me, while I debated with a Phillies fan over RBI's, hot months, and who we assumed played better defense. We didn't know wtf we were talking about when looking back in hind-sight.
Then the infamous comment, RBI's are based on your team, not the individual player. So I listened, this argument supported what I wanted (Pujols to look better) and that stats like UZR etc show that Pujols is a superior defensive player (not fielding percentage). These guys kept explaining why I was 'in the right' without knowing why I was right.
That is where it started, and since then anytime I want to learn something, those two guys are who I listen to first. They too have changed and grown in their baseball knowledge, and they are not rude about their opinions (very good linguists) and say their opinions clearly and concisely.
So I never had the chance to be resistant, because the argument I wanted to win, I was already on the correct side for, I just didn't know why yet.
Eventually things like WAR, and wOBA became better well known for me, and the rest has become history. I enjoy learning more and more, but overall, saber-metrics as a whole is a little overwhelming. Just because there is so much out there, and to chisel stats away one at a time is really the only way I can try to keep up. For the most part, I am saber-ill knowledged, but I know it well enough to get around.
At a buddy's house a few saturday's ago (BBQ) and we are sitting around talking baseball. Guys I grew up with, played baseball with through high school and college, and somehow my bro-in-law and I go onto the topic of Lance Berkman....then the word saber-metrics was said, and two of my friends (my age, 27, consider themselves baseball enthusiasts) said ......'what the hell is saber-metrics?'
How can you be such a big baseball fan and not have at least heard of it?