S.W.
My daughter (now 8) and I have been training in Karate for three years. I previously trained in Tae Kwon Do for five years. Each martial art has a slightly different approach but most include self-defense, forms (kata), sparring, and basics. Some use more kick/punch techniques and some use their opponents weight and movement against them and are more defensive.
I am a proponent of all martial arts training for children and taught a children's class for two years (but am partial to TaeKwonDo/Karate as you can tell). I would recommend choosing a few schools that are conveniently located, with class schedules that would work for your family, and visit during a class that includes six year-olds. All reputable schools should encourage this. I would observe, and talk with parents who are there about their experience. A good school will emphasize that these techniques are for use in class and for self-defense and no other times. Good teachers should expect respect and consistent attention from their students, but should also be encouraging and able to have occasional fun in their classes for kids. There should be some flexibility in their program as far as required/encouraged attendance, and belt level promotions should depend on skill level and not just attendance.
I would recommend getting all the details about pricing - what is included and not included - some charge extra for uniforms, belt exams, tournaments (typically extra and optional). Ask if there is a trial period (my school offers a two week trial period) and/or an introductory lesson so your son can try it without no or a small financial commitment.