I applied in-person. The process took 4 weeks. I interviewed at Brigham Young University (BYU) (Provo, UT) in Jan 2015
Interview
It was offered to me through a French professor. I applied for the job and each applicant received an interview in the language they were supposed to teach. This all happened within a few months' time. It was a pretty selective process since SI's are generally pretty well protected in their positions, provided they do a good job in teaching their language. This was a position for teaching French 101 at BYU.
Interview questions [1]
Question 1
I don't remember the questions they asked. I'm pretty sure it was pretty basic; questions about your background, why you would be a good fit, what you are studying (besides the language you want to teach), and where you see yourself in five years.