On campus interview after application was submitted; I was part of a prospective student visit, along with three other students. I sat in on classes, met one on one with the chair, and had lunch with students and the other prospective students. Whole process was geared to be informative rather than competitive.

Straightforward: questions about why you're applying to Columbia, your research plans, etc. Be prepared to listen actively to any information/anecdotes interviewing professors may offer and have some interesting, thoughtful questions to ask