I agree with the suggestion to do ImagiNations - it's a great experience, whether you get a prize or not.
For more ideas of how the Imagineering process works and what each person does, you might want to try reading Walt Disney Imagineering: A Behind The Magic Look at Making The Magic More Real, the recent update to an older book with a lot of new material.
Also, depending on your budget, there's a course called the Theme Park Design Workshop. It costs $200 and isn't affiliated with Imagineering directly, but Steve Alcorn who runs the class used to be an imagineer and he makes a lot of equipment for them now. (His company, Alcorn-McBride, makes the show control system that most of imagineering uses, and his wife still works there.) I can't post links yet, but if you search for Theme Park Design Workshop or Imagineering Class, you'll find it.