Baseball, by the Rules
For more examples, click here.
Called Ball
The pitch comes in, the batter does not swing, and the umpire judges that the pitch did not cross the strike zone. The catcher and/or pitcher thinks “what the heck, that definitely caught the zone,” and they feel confident enough in their judgement that they initiate a challenge.
The only people who can challenge a called ball are the pitcher and catcher1 on the field, and they must make that decision “immediately” after the umpire makes their call. “Immediately,” here, is supposed to mean somewhere within a second or two. Also, neither the pitcher nor the catcher are supposed to have “assistance” from anyone else, especially anyone in the dugout2. If either the time or assistance conditions are violated, the home plate umpire can turn a challenge aside.
To challenge, the pitcher/catcher taps the top of their head (though catchers will sometimes challenge verbally rather than via gesture). This cues the home plate umpire, who turns around to signal to the replay booth that a challenge has been initiated (and accepted). The replay booth plays the review, and the umpire announces the result. The entire process is designed to take as little time as possible.
The ABS system's rules for what counts as a ball are the same as the home plate umpire's... mostly. What's the same? As long as the ball does not touch any part of the strike zone, the pitch counts as a ball. The difference, is that the ABS system only looks at a two-dimensional plane, rather than the three-dimensional strike zone that the rulebook spells out. So, yes, it's theoretically possibly for a pitch to clip the rulebook strike zone, but miss the plane that the ABS system is surveying. Such a pitch would likely be called a ball3. It's certainly possible that one day in the future, MLB will iterate its way into a three-dimensional ABS strike zone, but for now, the strike plane is all we have.
Ultimately, the ABS is either going to confirm the, um, ball call, or overturn it. If the call is confirmed, the result of the pitch stands, and the definding team loses a challenge. If the call is overturned, a ball in the count is turned into a strike, and the plate appearance continues (or doesn't, if the result is a strikeout). The defending team retains the challenge, and can use it again as soon as someone feels the need to.