STEP ONE in choosing a school is to clearly understand what you want you or your child to gain from learning the Martial Arts. Is it a light recreation? Then a community center program may suffice. Is it self-defense or personal development? If so, then a full time professional school would be more suitable. Many parents view the martial arts as a part of their child's educational development. With a good professional school, this is very possible.
STEP TWO is to recognize that choosing a school is really choosing an Instructor. Be sure to visit the school and watch the Instructor work with other children of the same age. Every school is very different because every Instructor is very different. Don't get confused by claims of Black Belt degrees, tournament wins or martial art styles. The only style that matters is the teaching style of the Instructor and how your child will respond to him or her.
AND LASTLY, trust your instincts. A professional school will have a family atmosphere, lots of smiles and be well kept. You'll feel comfortable with the personnel and the facility. While this may not end up being the closest school to your house, when it comes to your safety or the safety and education of your child, an extra ten-minute drive can make a world of difference in the outcome.