Yeah the AL/NL thing isn't actually very complicated. Both the American and National leagues are under the MLB (Major League Baseball) umbrella, and as Revson said, for the most part, AL teams play other AL teams all season long, and NL teams play NL teams. Neither league is considered superior to the other as far as professional talent goes, and it's not unusual at all for a player to be traded, signed, etc across league-lines over the course of their career. I don't really know the history of how the current league arrangement came to be, but growing up in Seattle and being a lifelong Mariners fan (an AL team), I've always paid the most attention to AL teams and I'm definitely most accustomed to the DH (designated hitter) in the batting lineup, rather than the pitcher in the batting lineup. Honestly, I think the DH is a much better system than making a pitcher feel obligated to regularly and actively work on his hitting, because pitching is immensely difficult in ways that hitting and fielding are not (both physically and psychologically). I think it makes the most sense to let pitchers focus entirely on their primary role with the team, and then let the team insert a non-pitcher into the DH roster spot for each game! NL teams make no consideration at all of a pitcher's ability to hit when signing them to a multi-year, eight or nine-figure salary...they sign him completely for his specialized pitching abilities, so why make pitchers hit at all?
Anyway, baseball is amazing! If you're interested at all, I highly recommend [ame="http://www.amazon.com/Thinking-Fans-Guide-Baseball-Edition/dp/189496330X"]The Thinking Fan's Guide to Baseball[/ame] by Leonard Koppett. It's excellently written and it really cracks open the fine details of the game, without reading like a boring textbook. I've been a baseball fan my entire life, and as I've gotten older, I've come to appreciate the game at a far more mature level than I ever did as a child. It's such an intense, mentally stimulating game for me...it's almost like a big game of chess, with each move being carried out by a field full of talented athletes. I'm fairly used to hearing people argue that baseball is just way too boring and slow, but someone who makes that argument is most likely just ignorant to the underlying emotions and strategies of the sport, or they just don't have enough of an attention span to really get engulfed into a sport that isn't totally saturated with endless quick movement. Even just starting to understand the underlying thought processes and strategies between the pitcher/batter match-up goes a long ways towards making the game come alive. Sure, the moments of actual action are very short-lived, relative to the length of the complete game itself, but there's a lot going on beneath the surface that simply takes time for most people to learn to fully appreciate.
Oh, and check out the movie
Moneyball if you haven't already seen it. Really well done, and it's also a good introduction to the role of
sabermetrics in baseball, which is pretty fascinating (and controversial to some), and has only been widely respected and employed in baseball over the last decade or so. Think of sabermetrics as basically economics-style equations, where you are measuring a player's skill set and evaluating their talent using mathematical representations of their in-game statistics. It can get really deeply intense and complicated, and I don't claim to be able to articulate all of it, haha...