Pre-Interview: Got an email from a recruiter recommending that I apply. So I applied online. Very fast and easy.
Phone Screen: Talked with a software developer at Epic. He discussed the company, and said some brief information about the position. He turned it over to me to discuss my experience, why I am interested. I just used the STAR interview procedure for answering the questions. He asked me one technical question.
Technical Round: After I passed the phone screen, I basically took an exam online that lasted a few hours. Just read the other glassdoor reviews on the technical round. They are very helpful.
Onsite Interview: Tour of campus, software demonstration, description of position. Three primary interviews: one case study (just be prepared to answer some easy questions about an application but also think outside the box), one interview about a project of mine, and one interview with an HR representative. For the HR interview, just practice the STAR interview technique. Also, be honest; if you are not a good fit, then you probably wouldn't enjoy working there anyway.
All in all, it takes about a few weeks total. I really enjoyed their tour of the Madison area and the campus. Their offer in terms of compensation and benefits is very hard to beat. They hire the best.
In the end, they called me and let me know they were considering me for the business intelligence developer position, which was more interesting to me anyway. My understanding is that the interview processes for the two positions are similar, if not the same.