I applied for the Chess Instructor position online with a simple email describing my experience with chess, my tutoring experience (emphasizing that I had worked with K-5 children before), and my approximate playing strength.
I was contacted over the phone by one of the teachers, who asked me about my interest in chess and my experience teaching or tutoring, and we scheduled an interview time. I was asked to prepare a chess game to go through (preferably a shorter one), and present it to two of the instructors as if I were teaching a class of elementary school aged students at the beginner to intermediate level.
I chose a classic chess game that wasn't too long and one that followed basic principles. Two of the teachers there observed and interacted with me, as I asked them the type of questions I would ask to engage elementary school aged children. I went into more depth than was probably necessary, but the two teachers said that as long as I understood that most of the kids were beginners, I would get the hang of presenting games and giving lessons pretty easily.