I'm really interested in learning about the game of baseball, since my grandpa used to be an amateur baseball player. 
I love baseball! It's played with a bat and ball - there's 2 teams each with nine players and they take turns batting and fielding
What's the goal of the team that is batting?
The team that is batting wants to score runs!  The more, the better!  
It sounds like a fun game to watch. Where are these games typically played at?
Baseball is played on what is called a diamond - and they usually play 9 innings unless the score is tied
What happens when they get to 9 innings and there is a tie? Do they have overtime like hockey?
Extra innings
Extra innings is the extension of a baseball or softball game in order to break a tie.
Ordinarily, a baseball game consists of nine innings (in softball and high school baseball games there are typically seven innings; in Little League Baseball, six), each of which is divided into halves: the visiting team bats first, after which the home team takes its turn at bat. However, if the score remains tied at the end of the regulation number of complete innings, the rules provide that
Baseball positions
Baseball is a bat-and-ball game played between two opposing teams who take turns batting and fielding. Within the game there are positions in which each player can play in. 
There are nine fielding positions in baseball. Each position conventionally has an associated number, which is used to score putouts:
1 (pitcher), 2 (catcher), 3 (first baseman), 4 (second baseman), 5 (third baseman), 6 (shortstop), 7 (left fielder