Prepare to get chosen for the Jedi Training Academy before you go to Disney's Hollywood Studios. Select colors that make your kids stand out like yellow. The shirts that seem to get chosen the most have Star Wars (Words or Rebel characters) or Disney characters on them. It does not not matter if your kids are girls or boys, they seem to choose slightly more boys, but there usually many more boys trying to get chosen than girls. It usually does not matter if they have a hat on or not. Although, most of the kids chosen with hats were some type of Disney hat (Goofey hats, etc), or Star Wars hat.
Arrive at the Jedi Training Academy stage early. Plan to get there at least 15 to 20 minutes before the next Jedi Training session. The Jedi Training Academy stage is past Echo Lake, in front of the Star Tours attraction. The crowds will get heavy along the fence line of the stage near the time of the show so get a spot for your kids in the front. Your kids should act excited about being there. I cannot confirm this, but it is a guess that the Jedi trainers are watching the crowd even before the show starts to see who they want to choose. If you get there right as the Jedi Training session is starting, your chance of being selected is almost zero, unless there are not many kids there.
Choose the best location near the stage. There are two good locations, where most of the kids are selected. If you are walking up to the Jedi Training Academy stage, the left side of the stage runs all the way back to near the Star Tours building. This side of the stage will also be closest to Darth Vader when he is fighting the Jedi trainees (although his back will be to you). When the Jedi Trainers come out they tend to start choosing from this location of the crowd, since the trainer can walk very near near side from the upper stage. Get a good location at the middle part of the upper stage on the left side.
The other location (facing the stage) is the right corner. This is right in front of the lower, ground level part of the stage. It is easy for the Jedi trainees (kids) to enter here so the Trainers tend to chose several kids for Jedi training near this location. Do not go behind the bushes in the far corner, stay further to the left.
It also appears that when they have two Dark Jedi like Darth Vader and Darth Maul, the kids chosen from the left get to battle Darth Vader and the kids chosen from the front get to battle Darth Maul.
Once you get a good location along the fence do not give it up. Make sure your kids know that they need to stay right in front until the Jedi Trainers pick all the kids. As the show time approaches, help your kids fend off other adults who will try to shove their kids in front of yours. Help them hold their ground by keeping your body in behind or beside them. Ask others politely to stop if your kids are getting shoved around. Not everyone you encounter in Hollywood Studios will speak English so do not start a fight if they do not understand you. If your kids are small pick them up or put them on your shoulders.
When the Jedi Training Academy Trainer comes out have your kids wave their hands excitedly and smile. If they are on your shoulders try to act excited, do not get angry or yell. The jedi Trainer will sweep through the crowd several times until they have chosen enough kids. If the Jedi Trainer points anywhere near your kids direction and says "you, the kid in the yellow shirt" get your kid out there as fast as possible. If both of your kids are wearing yellow, push them both out there. The trainer will take them both. I have seen trainers say "you the one in the blue shirt" and 3 kids have gone out on the stage and he took them all. If your kids stand there and say "Me?", then two others kids might go out and they will have missed getting chosen for the Jedi Training Academy.
