Applied online through the Stanford Careers website. Several days later, I was asked to fill out an additional questionnaire. Notable questions included the two listed below, as well as a question that essentially asks for things you'd have put in your cover letter anyway.
I had an initial interview with two supervisors a week later. A mix of standard interview questions (why do you want to work here, why are you leaving your previous job, what do you bring to the table), some old-school questions (what are your 3 greatest strengths? your 3 weaknesses?), and a discussion of what specifically the job entailed. This lasted one hour.
The second interview lasted around 1.5 hours. First was a panel interview with the supervisors and 5 people in the position I was applying for. Again, very standard questions, with some behavioral "how would you react to X situation." One interviewer asked me to give an impromptu explanation of a chemical concept at a level understandable to novices to the field. I was also given the chance to ask the interviewers questions about their experiences in the position.
Afterwards, I was given a Standard Operating Procedure to quickly look over and give my thoughts on it to the supervisors.
Another week later, I had a third interview with the supervisors where they asked me to address some concerns they had about hiring me - mainly about the transition from an academic environment to a more rigorously scheduled workplace. Later that day, HR contacted me and offered me a position.