When the park opens, head left and go past the American Idol Experience, stopping at Sounds Dangerous--you'll see the newish sign-up area--you'll go in and wait in line with the child who wants to take part. Kids are placed in groups of around 15, with shows starting about an hour after the park opens and going to around 5:30; groups may be larger during busier times of the year and shows may go later. The cast member may ask your child a couple of questions, such as how old he is and if he can follow directions. Then, they'll hand you a piece of paper with your child's name on it and a return time, which will be 30 minutes prior to the next show.
The new sign-up process works very well, but make sure you get there within the first hour or so of park opening (not an Extra Magic Hour opening, but the regular park opening) or you run the risk of that day's shows being filled. The only dilemma you'll face is whether or not to go there first or rush over to Toy Story Midway Mania. Since TSMM fastpasses tend to run out before noon, my advice would be to split up, with one adult running over and getting fastpasses for your group and the other taking the would-be Padawan over to JTA to sign-up. If you get there right away, you should be in the first or second show and will also likely be in the TSMM fastpass time frame after the show. If you're not, you can still use your fastpass later in the day.
Since it was just me and my son, we rushed over to TSMM for fastpasses and then made it in time to sign up for the second show, which was set to begin at 10:50. Our fastpass return time was from 11:45 - 12:45, so it worked out perfectly. The only time I can see running over to TSMM first this being an issue is during the very busiest times of the year, when you run the risk that all the available slots will be full before you make it over there.
Now in the immortal words of Master Yoda: Train you will, young Padawan.