I applied online. Shortly after, I was invited to take a personality test. They notified me one week later that I would have a telephone interview. The phone interview was with a project manager and started out with me asking the questions. It finished by him asking some very basic questions, none harder than, "What's one experience on your resume that has best prepared you for this position?"
Then I was invited to take the skills testing at a Pearson center. You have to sign a confidentiality agreement, so I won't go into what was on the test. But you can't study for it and it isn't all that difficult.
One week after I took the test, I was invited to Madison. At Madison, there are a bunch of informal activities that don't seem to weigh on their decision. You have dinner with two employees the night before, lunch with an employee and a handful of other candidates, a tour and a product demonstration. It doesn't seem like the employees at these times are really assessing you as a candidate, but obviously, be on good behavior.
There is a ridiculously easy case study. You'll be taking it with one other candidate, so be sure you brush up on your group interview skills before you go out to WI. There's also a 1:1 interview with a project manager. I really enjoyed this interview. They pick a few things out from your past and you talk about it for a half an hour. It was very laid back, but at the same time, I think a very useful interview for them. There's also an HR interview, which is filled with the usual fluff questions: "What are five things you're not?" "What's a negative and positive thing each of your references would say about you?" "Where do you see yourself in five years?"
There's also another testing session that day. I won't go into it, because I can't, but I thought it was significantly harder than the pre-interview testing.
I didn't get an offer, which wound up being a good thing. Living in Madison just isn't for me. While it's a nice little city, it's a little city nonetheless and I'd be very bored living there.
A few things struck me. The dress code is very lenient -- one of my interviewers hadn't combed his hair and was wearing a t-shirt that almost looked dirty. You'll be most comfortable interviewing in khakis and a polo shirt or a dress shirt without a tie.
Another thing was the discordance between the people in the job and the candidates. The candidates mainly came from state schools, while the people that interviewed us tended to go to highly ranked private schools. I'm not sure how much stock Epic puts in your alma matter.
It was also clear that this was a temporary position. It's really clear why people don't stick around for long. The hours seem very long and the travel sounds like it'd get burdensome. Most of the people interviewing me had been there for fewer than two years, some less than a year.
Good luck!