Get the ASA Umpire Edition of the rulebook (assuming it's ASA) or another organiation's rulebook/umpire manual. Read it like crazy - it's likely it will answer many of your questions.
As for calling balls and strikes, make sure your are locked into the SAME position for each pitch (consistency, I'm sure you know, is key). The strike zone is probably the hardest part of umpiring, and if your getting it down in your first game, I know you're definitely superior to me!
Good luck and welcome to the board!