You can ask around for suggestion in this order:
- ask your friends
- ask parents of any kids who play chess
- ask our school, especially when they have an after-school chess club
- ask your local library or nearby libraries
- check township newspapers, especially when you look for summer camps
- ask any teacher you meet (he or she may be living too faraway, but s/he may know some fellow teachers who live close to you)
- ask local chess clubs
- ask your state chess federation or association
- ask online
When introducing kids to chess, stimulating the kids' interest is more important than infusing skills. Make sure your kid likes the teacher, otherwise switch as soon as possible. Do not expect fast progress. Most kids need time to get used to playing chess. As long as they want to play and like to play, they are fine. The keyword here is persistence.
If s/he starts to play in tournaments and become serious with her/his chess development, you will need a rated teacher who has experience with scholastic tournaments. 500 points gap is the least you should look for and minimum rating should be 1500. You want to search for good teacher or coach in this order:
- ask other serious students and their parents
- ask other coaches when you go to tournaments
- ask local chess clubs
- ask your state chess federation or association
- search teacher lists on ICC (chessclub.com)
- search coach directory on chess.com
- ask online