Getting an interview at Disney is the hard part. They often fill posted positions internally and rely greatly on references. Try to track someone down at Disney to refer you when you apply for a job. The interview process starts with a phone interview from HR, then they bring you in if it seems like a fit. The whole process from the HR call to an offer can take a long time - probably 4 to 8 weeks.
My interview was fairly long. I met with 4 different people, 30 minutes each. Questions were standard. They like to make sure you're a fan of the Disney brand and that you've had experience working on brands with strict guidelines. There are a lot of people at Disney who live and breathe the brand, so try to be excited, upbeat, and positive. They might ask questions like "What's your favorite Disney character?" Culture is very important to them. Make sure you don't dress overly formal. The people who work there tend to be friendly, confident and warm.