I haven't seen JTC at WDW, but my daughter did it at Star Wars Celebration II, last May, and I believe it is the same thing. It was running every hour or so most of the convention, It took my daughter 3 tries to get picked. She didn't do anything special, just stood up and raised her hand. I think he chose around 5 or 6 kids each time.
The entire thing probably lasted about 15 minutes. The kids go up on stage and are given robes and plastic lightsabers (same kind you see at any toy store.) The "Jedi Master" has a script that he seemed to follow very closely each show. Mostly he says things that Yoda said during the movies. He teaches the kids a series of moves with the lightsaber ("block high," "duck," "cut low") and they learn them in a specific order. They run through it a few times, until they all have it down.
Then the Imperial March plays and two stormtroopers come out, followed by Darth Vader. The Master tells Darth that these kids are pure and will never join him on the Dark Side, then the kids go up one by one to duel Vader. The Master calls out the moves in order so the kids can remember what to do. It's like a choreographed fight. When all of them are done, the Master announces that Vader has been defeated and the Sith Lord marches off in a huff. Then the kids all get certificates.
My DD was 4 at the time, and he seemed to avoid picking anyone younger than that. One toddler, maybe 2 yrs, inserted himself onto the stage without being picked. The mom seemed to have no problem with this, and the Master was too polite to say "get him out of here." The child had no idea what was going on and left the stage in the middle of it. I don't remember any kids older than maybe 7 or 8 doing it, but there may have been some in other shows we didn't see. Any older than that would probably think it was kind of lame.
T