A ball that hits or ends up on the plate is no different from any other batted ball. The relationship of the ball to the foul line at the instant it first reaches the ground, or where it first contacts a fielder, determines whether an outfield fly ball is fair or foul. If a ball strikes the ground before reaching the fielders - even if it bounces before coming to rest - it is considered a foul ball. Balls that hit the ground in front of the stands but don't touch the fielders are still considered fouls as long as they don't bounce back into the playing area.
Balls that hit the ground behind the stands and don't roll away are dead balls and should be thrown by the umpire-in-chief once he has called time. He will usually call for gloves before doing so. This prevents spectators from retrieving balls that have fallen behind the stands.
Fair balls are those that land outside the foul zone. An outfielder has no legal right to catch such a ball, but may do so if he wishes. If a ball is caught by an infielder, it is considered to be alive and should be thrown to another infielder for safekeeping. If it isn't, then it's a double.
Now, there are two ways a ball can reach the stands.
When a player touches the hit ball in fair territory, the ball instantly turns fair. The ball stays in flight until it makes contact with the ground—touching a player has no effect on this. As a result, this regulation applies. It is a foul ball if a fly ball is first touched by a player in foul territory and then travels over the fence.
In addition to these rules, each league may have additional rules regarding fair balls and foul balls. For example, your league might require that all foul balls be thrown back into the game.
The only way to determine if a ball is a foul ball is to check with the umpires. They will tell you if there was foul territory near where the ball was caught/thrown from and if so, it is a foul ball. Otherwise, it is a fair ball.
It is important to note that even if a player appears to have interfered with a ball, he can still reach out and touch it before it reaches the ground. If he fails to do so, however, it is a foul ball.
A fair ball striking the top of the outfield wall and bouncing back into the playing field is handled the same as a fair fly ball impacting the outfield wall and rebounding back onto the playing field, unless differently specified by a local ground rule. If the ball goes over the fence, it is in play at its highest point. If not caught before it hits the ground, it is a lost ball.
If the ball strikes the wall and comes down inside the park, it is dead ball territory for the batter. He can take as many pitches as he wants from the pitcher, including balls and strikes. This rule applies only if the ball does not leave the park. If the ball goes out of the park but is caught by an outfielder, it is a double.
If the ball bounces off the wall and away from the field of play, it is a foul ball. The umpire(s) will call time and signal for a new ball game. This rule applies even if the ball goes over the fence; it's still considered to be a foul ball because it went beyond the field of play.
If the ball hits the wall and comes down outside the park, it is a home run. The batter and all offensive players are given permission by the home plate umpire to enter the field of play for a home run celebration.
It's a foul ball if a batted ball strikes the plate first. Home plate, first, second, and third base are all totally within fair area, according to the approved ruling. The foul lines are also on fair ground. To be ruled foul, the ball must come to rest in foul area or be touched in foul zone. A batted ball that does not strike the plate is still considered part of the game and may be handled by any player including the batter. These balls are called wild pitches.
A fair ball is one that hits the plate cleanly. It can be caught without moving your feet. Wild pitches and bounced passes are examples of fair balls that don't hit the plate. Batsmen try to get men on base by hitting them with pitches. When this happens home plate umpire signals that there will be a walk. There are three ways for a batter to get a walk: he can reach first base before the pitcher begins his delivery from the mound; he can be awarded a base on an error; or he can be given a pass when the catcher drops the ball (leaves it in his glove).
Fair balls are easy to judge because they carry no momentum and so do not travel far. However, foul balls tend to be hit with great force and so carry much more speed when they reach the field. Thus, they travel farther than fair balls.