Third Strike Not Caught (TSNC) Or Uncaught Third Strike
Rule 6.09(b) -
[for baseball and softball majors/intermediate/junior/senior divisions:] A batter becomes a runner when the third strike is not caught, providing (1) first base is unoccupied OR (2) first base is occupied with two out.
NOTE: A batter forfeits his/her opportunity to advance to first base when he/she enters the dugout or any other dead ball area.
Comments:
There are several correct mechanics involved here that are important for the umpire to get right. The proper signaling mechanic is to extend your right arm and hand out to the side pointing and making no sound. This is to ensure there is no confusion on whether the batter is out or not. As an umpire, you can append several signals to this mechanic to help managers and coaches now if the batter has been tagged or not tag at the plate if the batter chooses to advance to first base. These mechanics are in the links below.