According to the ASA Rules Supplement (R/S #1), there are four situations that warrant an appeal:
1) Missing a base, or touching the white portion of first base when a play is being made at that base,
2) Leaving a base early when a fly ball is caught,
3) Attempting to advance to second base after making a turn at first,
4) Batting out of order.
A live ball appeal occurs while the ball is live (duh!) and is frequently part of the play for an out. For example, if a runner rounds first then stops and tries to return to first but is instead tagged by the first baseman, this is actually a live ball appeal and the batter is out if the umpire judges that the runner tried to advance to second. Because the ball is still live, any other runners may advance at their own risk while the appeal play is being made.
A dead ball appeal occurs…wait for it…when the ball is dead, but before the next pitch is made. First, the umpire waits for all runners to finish their base running and the ball to be in the infield in a fielder’s possession, and then calls “Time!” Once time has been called, any infielder (including the pitcher or catcher) with or without the ball can make an verbal appeal on a runner missing a base or leaving a base early on a fly ball. A fielder merely has to say to the appropriate umpire something to the effect of “I make an appeal on the runner at third leaving the base early before the fly ball was caught.” The appropriate umpire then makes a decision on the play. This is definitely less of a headache than appeal plays of my youth.
A dead ball appeal can be made for a fourth out in the inning if a runner who scored on the play ahead of the third out missed a base or left a base early on a fly ball. The fielders must remain on the field between the foul lines to make the appeal. In the case of the last out of the game, the umpires have to be on the field for an appeal to be made (the umpires will leave the field immediately once fielders cross the foul line or end-of-game celebrations have started).
Batting out of order is always a dead ball appeal, and one reason why a good scorekeeper is a coach’s best friend. If your team is the offensive team, it is best to make this appeal during your player’s at-bat so that your team does not absorb an out. If the appeal is made during the at-bat of the incorrect batter, then the correct batter assumes the at bat with the current count.
If your team is the defensive team, then it is best to wait until the at-bat is over and before the first pitch to the next batter to make the appeal. If the incorrect batter finishes the at-bat and the appeal is made, then
1) the batter who should have batted is called out,
2) all runners who advanced because of a hit or walk by the incorrect batter must return to their original base,
3) the next batter is the one who follows the batter who should have batted.