Batter's box - Batters must remain inside the batter's box. If they hit the ball while outside the batter's box, they are out. Leagues may have different rules as to how far out (the entire foot for example) is considered outside the box.
Hit by pitch - If the batter is hit by the pitch, then they are awarded a free trip to first base. There are a few rules where getting hit doesn't count as a "hit by pitch": if the player is hit as a result of swinging for the ball, if the player gets hit in the strike zone, if the player doesn't try to get out of the way of the ball, and if the ball hits the bat first and then the player. In these cases, the pitch is called a strike.
Dropped third strike - When there are 2 outs or first base is open, the batter may attempt to advance to first base if the third strike is dropped by the catcher. In this case the batter may try to get to first base as if he had hit a fair ball. The defensive team may try to get him out just the same, either by force out at first or tagging him out.
If a player is on first base and there is less than 2 outs, the batter is out whether the ball is dropped or not.
Pitching Rules
Number of pitches - Many youth leagues have the rule that a pitcher may only pitch so many innings or number of pitches per week. These rules should be followed as they are meant to protect young arms from getting injured.
Balk - Pitchers must pitch with one foot on the rubber. Once they are standing on the rubber or with one foot on each side of the rubber, they can only make certain motions or they will be called for a balk. A balk only is called when a runner is on base. If a balk is called, each runner is allowed to move one base. The balk rule is very complicated. Some of the illegal balk motions include:
Starting to pitch, but not finishing the delivery.
Dropping the ball while on the rubber.
Standing on the rubber as if preparing for a pitch without possession of the ball.
Making a quick pitch in attempt to catch the batter off guard.
Not making a complete stop with hands together while pitching from the set position.
Makes a fake throw to first base from the rubber without throwing the ball.
