Got pointed to Epic by a colleague and applied for a general software developer position. Received directions after a week to take a personality/math skills exam.
After this phase, roughly a week later I scheduled phone interview where I was asked some general questions about my work and told about the position. You'll get pretty standard interview questions about your strengths/interests/plans.
Got confirmation to take a programming exam at a local testing center about a week later. My advice: just brush up on your basic skills like recursion, permutation, and keep the code simple. The whole things takes about 3 hours.
A week or so later got confirmation that I'd be visiting the campus. They do a great job of taking care of you while you're there. All the cabbies know about Epic, so transportation is super simple. It's a little daunting being thrown around with a bunch of other recruits (there were over a dozen in the hotel I stayed at), but don't worry, you really aren't competing. Had a relaxing dinner with an employee and 4 other recruits near the capitol.
The interview day at Epic is epic. After a software demo and campus tour (take the slide), you'll interview with a number of employees, both to learn about positions and for them to get a feel for your thought process. There's not a whole lot of down time, you're dropped off from one interview only to be picked up by the next. My interviewers were very pleasant, you'll get some questions to see how you think and manage people. At the end of the day, there is an interview with an HR rep, where you'll discuss basic employment topics from your application (salary, group preference, etc). You get a timed 2 minute math/verbal test at the end of it to get you "re-geared" to take SAT-type math/logic/verbal tests. These tests take about an hour or so and they get you a cab to the airport. They usually get back to you in 1-2 weeks, after checking your primary reference.
It's certainly a long process so patience is a virtue; from application to offer took 2 months. The place is like Neverland: the average age is 27 and there is nary a grey hair to be found. Definitely not for professionals, but if you're within 5 years of the average age (and a graduate) and have people/tech skills, it might be a good fit for you.