A friend of mine who works at Epic submitted my name through Epic's internal referral process. (I highly recommend this to anyone interested in working at Epic. Your contact will get a bonus for successful referrals, and you are four times more likely to get hired.)
I was emailed by someone in HR and sent links for online assessments and position application. About two weeks after completing all of that I had a phone interview. At the end of the interview the interviewer scheduled a day the following week for me to fly out to Madison and interview in person at their Verona campus.
The night before the interview I was taken to dinner by an Epic employee along with several other applicants. This was a chance to ask questions without worrying about the person being in HR. (Really this person does not make any hiring decisions, so try to relax a bit.)
The day of my interview I took a shuttle from the hotel to the main Epic campus with several other applicants. Once there we were given a tour by someone in HR and told all about Epic. The campus is really cool, so the tour was a lot of fun.
I was applying for both a project management and training position, so I was interviewed by a project manager and a trainer. I also gave a 20-minute presentation to an audience of four employees to showcase my presentation skills. The topic of the presentation was up to me.
After the interviews I took a number of written evaluations. I can't give any details about the evaluations, but I can say that they are quite challenging and there is really no way to study for them.
After completing the evaluations I had one more interview with someone in HR. That interview lasted about 20 minutes. After that I was able to take a self-guided tour of the campus before taking a taxi to the airport.
It took about two weeks to hear back on the job. When they offered me the job they told me how much the job paid. There was no pay negotiation, which was a relief. The amount offered was actually much higher than I would have asked for.