First, you're starting a little late. Teams are in playoffs. The way to approach is to ask if player can skate with team at a practice. Usually that's done in January and Feb. It's helpful if there's someone who can make the intro to the coach and vouch that the player is decent and family is "normal" (not distruptive jerks and not shuffling their player to a different team every year). Some coaches don't care about those points. IMO you don't want your kid playing for a coach who doesn't care. Even though it's a little late, see if you can get an intro. Tell coach why you are interested in that team (good reputation of coach, good experience of a friend, etc). Good luck. 🍀
Unfortunately, the key piece of advice is to start in January or February. That's not to say the aren't still opportunities, but very few practices left in the season.