Helpful tips on finalizing your decision:
1) Ask for referrals. Get the input of experienced parents and veteran skaters.
2) Observe other skaters' lessons. See how skaters interact with their coaches. Is their dynamic what you'd like for your skater? Does the coach consistently produce high-quality skating?
3) Talk to the coaches at your surrounding rinks! Ask them about their experience, credentials, their teaching methods and their coaching outlook. Does their philosophy seem to line up with yours?
4) If you think you've found a good fit, schedule a few trial lessons. See how your skater works with that coach, and ask them how they like the lessons. Keep note of how your skater is improving. If you think you've found the right coach - congratulations!