Make sure to have researched what Ad Ops (or your respective position) is all about. And get a sense for what the LinkedIn culture is like..
The entire process took a little over a month. First interview was really laid back (on phone) with a campus recruiter (I got the interview through applying online//referral). She was very nice and told me where we would go from there. It was just a general screening.
2nd interview a week later (on phone) with someone from the Ad Ops department. Again, pretty standard, I talked about some projects I had worked on in school. Gave examples of what was frustrating with the project and how I overcame it. She was also very nice just like everyone else.
3rd interview was with three "higher up" people in the Ad Ops department via skype. It was one at a time, 20 minutes each. I walked them through my resume, told them why I was interested in linkedin and the position itself and so on. They also asked where I see myself in the future, and about projects in school. Not any behavioral questions at all.
I was supposed to get a decision after that but it seemed they had a hard time narrowing it down to the final candidate. So they scheduled one last (a fourth) interview with me with yet another on-phone interview. I feel I did well in this interview, same as the rest. I emphasized my working-in-a-team experiences.