In the NFL, the replay challenges are normally up to the head coach, who hears from his assistant coaches about whether or not they have a chance to win. According to ESPN on April 3, the MLB replay system seems to have an even better gauge to decide whether to challenge a call or not.
According to Texas Rangers' manager Ron Washington, it is about taking his time when walking out onto the field to argue a call. He said that while he is walking up to the officials, he needs to slow down and make sure he takes his time getting there.
That is because there is advance scout Joey Prebynski, a man who has access to all the camera angles that were shot of the play. He has trained himself to know which camera shows what so he can quickly look at the play and decide if the call was right or wrong.
Washington said that he gets to the umpire and then just asks what they saw. He then checks his dugout and gets a hand signal telling him to challenge or not to challenge, or possibly that it is inconclusive. He then lets the umpire know that he will challenge, or in one case in the Texas Rangers vs. Philadelphia Phillies series, he will laugh and say that they "won that one."
Washington said the umpires have been great in this implementation.
Honestly, one of the best things about the new MLB replay system is that teams with a setup like the Texas Rangers will know when they are right or wrong and this could easily eliminate a large amount of ejections and hard feelings between umpires and managers in the future.