The school tends to hire people who are connected to current employees. Advanced degrees, from prestigious East Coast/Ivy League universities tend to impress them. If you've taught/worked/coached at a private boarding school you're likely going to be fast-tracked to the top of the pile. If you're a friend of a faculty/staff member and you have strong credentials, you'll get an interview at a minimum. The actual interview process itself is pretty straightforward. Phone interview with the Assistant Head, followed by a campus visit for finalist candidates. When on campus, you'll meet with the Assistant Head, visit classes, and conduct a demo lesson. At least 3 administrators will be in and out during your demo lesson, as well as teachers from your discipline. If you're a diversity candidate you might expect an offer on the spot, but they've slowed down the hiring process a bit.