I started playing DnD when I was five years old. I read much of the PHB and sat in on my older brothers games to get the rest of the ideas. A friend of mine and I got a group and we went for it.
As for first hand suggestions, here is the big one. Let the child make the character decisions. Don't force anything and explain things so they have a "wow" factor. If you make one class sound better than others, they'll take that one and not have as much fun as when they get to pick from a balanced selection.
Number 2: I LOVED rolling dice. The bigger the handful and the more times I rolled the better (don't ask me why, cause I don't know). Maybe your kid will enjoy it to.
Number 3: Don't treat their character any different. If they do something that puts their character in trouble, play out the trouble. They'll appreciate "being one of the gang".
Number 4: Rubber rules. The more stringent the rules, the less interesting the game. This holds for all players in my opinion, young, old, newbie, or old-timer.
Number 5: This is by far the MOST IMPORTANT RULE. Make sure the child knows that it is a game. Kids have vivid imaginations. That is why they make some of the best players, but that imagination can run away with them. If they realize that DnD is just like video games and TV then everything is better.
I've been playing RPGs for 15 years now and I follow all these rules even now-a-days with any group I play with (even Rule 2, I love those dice

). It's all about fun and that's what kids want.