I applied through a career fair held at my university.
First round was a phone screen, which was a "get to know you better" sort of interview.
Second round was a timed online skills test (I believe you can take them offline as well), which tested programming knowledge, learning ability, quick thinking, and outside of the box thinking. This round was the toughest part, but I thought it was pretty enjoyable overall. There is not much you can prepare for, which is a sign of a good test.
Third and final round was an on-site interview. If you've gotten this far, you're pretty much guaranteed a position (as long as you don't screw up). Epic flies you out to their headquarters and gives you a pretty nice tour of their facility. There is a really simple one on one interview where you're asked to describe a project you've worked on.
Once complete, you should hear back within two weeks.