If you're talking about an appeal of a runner missing a base, or leaving a base before a fly ball is caught, the proper procedure is as follows:
After play has completed, the pitcher, with the ball, steps on the pitching rubber and comes set. He then steps off the rubber legally and throws the ball to a defensive player near the base they are appealing was missed. This player then steps on the base. If the appeal is granted, the umpire will impose remedies as appropriate. If the appeal is denied, the umpire will so indicate. Note: an appeal is made while the ball is live. This means that any other runner may advance at their own risk.
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There are 3 way to appeal in Baseball ....
(1) a right handed batter check swings and the home plate umpire say he did not go around ... the catcher will appeal to the 3rd base umpire... because he as the best view of the bat braking the plain of the plate...
(2) a left handed batter check swings and the home plate umpire say he did not go around ... the catcher will appeal to the 1st base umpire ... because he as the best view of the bat braking the plain of the plate...
(3) the runner missed the base (bag) and runs to the next base ... the fielding team will call time and tag the base that they think he missed ... the umpire for the base in dispute will render his decision as to the runner touching the base (bag) or not ...
Improving the answer:
There are other calls that can be appealed, such as "did a runner leave early on a flyout". On a play such as this you can just throw it to the base you feel the runner left early and they can make the call out or safe. In an official appeal such as the scenario above where the runner misses a bag. For an official appeal the pitcher will get on the pitching rubber with the ball, step off and throw to the base in question and the umpire will make the call. This cannot be done with time called, as the ball must be live. Some leagues will allow it to take place under time, however, this is not proper and should, by the rules, not be called by the umpire --- if the pitcher steps of the rubber incorrectly a balk should be called, if the throw is mishandled or overthrown runners can advance just as any other play. Once a pitch is thrown to the next batter, you cannot appeal the previous play