The process started with an email from my university's recruiter, who asked if I would be interested in interviewing for an internship at Microsoft Foundry in Cambridge, Boston. I had given my resume to them at the career fair a few months before. We decided on a time for a phone screening in the next few days, which went really well as he was great and made it into a friendly conversation. He then asked me what position I'd be interested in interviewing for (I chose design).
A month or so later, I traveled to Boston for my interview. Microsoft paid for everything. The other interviewees and I gathered in a room overlooking the Charles with the two recruiters who were managing our group. Throughout the day food was provided for us in that room, including fruit and desserts. For the designers, we started with a 15-minute panel where we each (individually, in a room separated from the other designers) presented a project we had worked on to three interviewers. They were all really nice and didn't make it stressful at all.
Then I had three 45-minute interviews, with short breaks in between (depending on the timing of other interviews). The first I had was with a guy working on the Office team. We talked a bit about my resume, why I wanted to do design (as I'm a CS student), and then he asked me to design the next Microsoft Band (v2, basically). I made good use of the whiteboard, tried to get a sense of the intended user and the current Microsoft Band, and then went off thinking of features that would be useful to them.
During the next interview, I talked with the interviewer about the Foundry, talked about working in teams and what I thought of it, and finally he asked me how I would redesign a website or software I know very well. I chose reddit, and talked about making it more visual, not losing the current audience, etc. I felt with this interview even more than the others that the whole conversation was about my thought process without directly asking design questions.
The last interview, I think, went best for me because the guy was so upbeat and friendly. I got to talk about some of my experience at hackathons, some more about my resume, and he then asked me to design a microwave for kids. Same process as before; try to figure out the user (and, this time, the customer). I focused a lot on safety and how the child would actually interact with the microwave.
In all the interviews, when it came time for me to ask a few questions of my own I would always ask what that interviewer actually did in the company, and went from there. All in all, it was a very positive (though tiring) experience, and everyone was exceptionally friendly.