Overall the process took about a month or around that due to the holidays.
I applied online and was contacted by a recruiter within a week of my submission. We scheduled a call for after the holidays so things could be easier for both of us.
The day of the call came and the recruiter was very professional and explained the process. He asked some of the basic questions,"Why Blizzard?", "Why this role?" After we hung up it took about two to three days to hear back from him informing me that the team wanted to schedule a phone interview.
A week later I was on the phone with two managers from the team. They asked some of the same questions but then really began asking how my skills related to the job, asked some very mechanical questions, questions about my current position, major tasks completed in this position, etc. Before we hung up, I was informed that it would be about two weeks before I would hear anything.
Within two weeks I was extended an invitation to visit Blizzard campus and have an in person interview. I arrived at campus and the check in was very simple and I was picked up for my interview. What I thought was one interview was actually two. One was with the team members and the other was with the managers again.
Dress casual!!!! A suit and tie is not needed and because of the length of time the interviews can take you want to be comfortable and the recruiter explicitly tells you this. They're not trying to trick you or mess you up.
After the interview I was given a brief tour of the campus before I said my goodbye(s).
The next day I was offered the position.
Overall, the process was decently easy. Use common sense and read everything that is sent to you by the recruiter. It will tell you everything you need to know.