About a week after applying, I had a 30 minute phone interview. It was with a person working in Technical Services who gave me the rundown of the position. It was pretty relaxed. Do some research on the job and company beforehand and you should be fine.
A few days later, I took a skills assessment which went over programming, math, logic and reading comprehensions in a few different test settings. Some of the tests were timed and others had no limit, but faster is better. Make sure to have a calculator (not on a phone). If you have a solid math and/or computer science background, it should be fine.
A few days later, I was invited to an on-site interview. This was really fun, they invite you to dinner the evening before and then the whole next day is spent at the Epic campus. Epic pays for the flight, transportation and reimburses extra costs if you keep the receipts. You have several opportunities to talk with Epic employees and people working in Technical Services. There were three actual "interview" portions of the day. First, I had an assessment to see how I would handle situations and prioritize my workload. Second, I had a standard recruiter interview. Third, I had a programming assessment.
I got an offer about three days after my on-site interview. The whole process took exactly three weeks from the day I applied.