When teams are in the position the Anaheim Ducks currently are in, and start interviewing for a head coaching vacancy, most of the time their short-lists are populated largely by former head coaches in the NHL (the Flyers hiring Alain Vigneault.)
Another common situation is a coach who is having great success in the minors and they think they can replicate that success at the next level (Jon Cooper in Tampa.) Less often, an assistant coach piques the interest of General Managers and they’re considered for head coaching positions (Phil Housely off the top of my head.