The rules are best picked up as you go along, I guess, apart from the basics.
I'm not sure I understand the second part of your comment, though. If the batter hits the ball in the air and it is caught by a fielder then he is out. It doesn't matter if the fielder is in fair or foul territory, he can even dive into the stands to make a catch!
Basic rules.
Each team has 9 players. (In the American League, the pitcher does not bat, but a 'designated hitter' bats but does not field. In the National League, the pitcher also takes his turn as a batter.) The game is played over 9 innings, each team batting in turn in each inning, away team first. When 3 men are out, their inning is over. If scores are tied after 9 innings, the game continues with even innings until there is a winner.
A batter who swings at a pitch and misses has a strike. A pitch thrown in the 'strike zone' - i.e. Over home plate and between the knees and the letters on his jersey which the batter does not swing at is also a strike. If he contacts the ball and the ball goes into foul territory, then it is a strike- but if he already has 2 strikes against him it cannot count as the third strike. 3 strikes and he is out.
If the pitch is outside the 'strike zone' and the batter does not swing, then it is called a 'ball'. 4 'balls' automatically allows the batter to walk to first base. Any runner on that base moves to second etc.
When a runner on base reaches home plate then a 'run' is scored. If a batter hits the ball out of the playing area within the foul lines and thus in fair territory, then it is a 'home run' and runs around the bases to home plate. Any runners already on base also run home and score.
If the batter hits the ball into fair territory he must run to first base before a fielder can throw the ball to the 1st baseman, if the ball beats him, he is out. Any runner on first base is forced to run to second base and can be out there if the ball is thrown to the fielder with his foot on the base, or otherwise in contact with the base, before he reaches it.
Those are some basic rules, I hope will help. But please ask any questions, I'll try to answer. Mlb.tv usually has a free game each day, so I recommend watching a game or two to get the general idea. Some games start at 1.05 eastern time, so 6.05 our time.
