First was a phone interview. Pretty basic stuff about your resume and related work experience. Also curious to see if you are willing to travel. If you pass that part, then there is a series of online tests. One deals with behavior, others with math and language skills, and one to see how well you would be able to learn programming or logic skills. Some questions were very, very similar to the LSAT, so practice logic games. Also, a review of grammar couldn't hurt. Be prepared to answer some of the questions quickly.
If you pass the online tests, you will be invited to interview at Epic's Intergalactic Headquarters (that's actually what they call it) in Madison, WI. It's a day long interview process, which is tiring but rather fun and very informative. You will likely have information sessions and a series of case studies, which are designed to evaluate your time management, teamwork, and problem-solving skills. No question was particularly difficult, but be prepared to explain your answers - they want to understand your thought process. Finally, you will give a 10 minute presentation on a topic of your choosing. They tell you about this a week in advance, so you have plenty of time to prepare. I actually thought this part was kind of fun. Finally, it's worth noting that Epic's facilities and employees are awesome. Everything is top of the line, and all of the people there could not have been more polite and helpful.
I am still waiting to hear back from them regarding their decision, but I visited less than a week ago, and they said that it would be 1-2 weeks before I would hear from them. Good luck.