Applied online to the "University Recruiting: University of XXX" posting on the Dow career website, although I graduated about 9 months ago, and have been working since. I was contacted within a week and scheduled for a phone interview. After a quick phone interview (about 25 minutes), I was immediately invited out for an onsite interview in Freeport, TX.
I gave my preferences for flight times and scheduling for the onsite interview; the Dow travel organization was quite accomadating, and I received the agenda for my interview day. I was reimbursed for everything related to the travel.
On the day of my interview, I first met with my "host," who was in the same role as the one I was applying for. She took me out to breakfast and then brought me to the facility, where I got a visitor's badge. I then had about 1 hour of interviews, 45 minutes with her and another automation engineer (slightly more senior), and then 15 minutes with the hiring manager (the regional engineering leader). None of the questions were tricky at all - just typical STAR-type questions. I was able to use examples from my current job, which was a similar position to the one I was applying for. I think this impressed my interviewers, and I felt confident throughout that I would get the offer.
Finally, we took a 40 minute tour around the Freeport facility (driving tour), then went to lunch. At all times, except for the hour of interviews, the atmosphere was extremely casual.