Applied online through college's career services website and was given an interview before the annual career fair.
The interview consisted mainly of behavioral questions, 'tell about a time you...' and lasted over an hour. The representative I met with was very professional and a little stuffy, but some of the others seemed to be joking around with their interviewees. Exxon went through many interviews. In the hour-long timeslot there were around 5 interviews being held simultaneously in different rooms, and spread that across 5 days of interviewing.
Most of the questions they asked had to deal with my previous work on projects, so I would recommend having something to talk about on that end. As I applied just entering my sophomore year, I really only had a simple freshman design project to talk about, so I think somebody who has had previous internship/project experience would do well.