DH - in the AL each team gets a 'designated hitter' that hits in place of the pitcher. im sure you noticed pitchers cant hit for shit. the NL does not have a DH believe it or not, which makes the rule weird, controversial yet cool thing about baseball.
player positions by numbers - see this pic:
you'll often hear sports commentators refer to a double play as 4-6-3 double play as in second basemen to short stop to first base (this is most common type of double play). for giants games here they show a players hitting night as F7 or flyout to 7 (7 = left field). you should know this as soon as possible.
strategy - this is where you gotta catch up just by watching a lot of games. hit and runs, when to steal, intentional walks, double steals etc.