1) Applied for an interview through my company's career development website; I was accepted
2) I applied on BP's website before my interview, as instructed
3) I had a 1:1 interview where the interviewer asked me a great deal about the research I was doing for my M.S. thesis. He also asked me some personality-related questions (standard fare: talk about a time you worked in a team, name your strengths, etc.). I also spoke about my previous Oil & Gas internships.
4) I had other offers, so I asked if they could let me know the results soon. Someone from Anchorage literally contacted me the evening of my first interview requesting I go to Anchorage for 2nd round interviews.
5) In Anchorage, there were some BP informationals (standard company fare), as well as a dinner for all those there with some ice breakers, etc. Next morning, there were three sets of interviews. I had to give a technical presentation to some senior reservoir engineers in the company (they allowed me to choose the topic; I was given prior warning before coming to Anchorage). Second interview was technical. I was presented with some wellbore dimensions along with fluid data and asked to describe how I would approach getting the most out of this well. Last interview was with a driller who gave me mainly personality-based questions. After interviews, we were given a tour of their Anchorage office. They took us all out for a nice dinner where employees gave their reasons why they thought BP Alaska was the best place to work. They came off as quite genuine. BP Alaska seems to have people who just genuinely love being in Alaska (most had been there for years, and a few had even turned down offers for international locations).
6) They called me the next morning after I had landed in Seattle (from Anchorage) and gave me a verbal offer. I applied for both Drilling and Reservoir Engineering positions, but they let me talk to employees to decide which one I wanted and then gave me a written offer.