I used to coach chess quite a bit. I've got plenty of pointers for anyone interested in learning how to do it themselves.
One of the more interesting things I tried was to start with king and pawn endgames. I'd start by teaching the kid how a pawn moves and how a king moves. Then I'd put a black pawn on e7, a king on e8 and a white king on e1. I'd say "let's play a game. If you get that pawn to the other end of the board, you win. You can restart the position as often as you want." After enough tries I'd start giving advice, but the first lesson never ended till the kid figured out how to promote that pawn.
This had two huge advantages. For one, instead of having to remember how six different pieces moved, the kid only had to learn one piece at a time. For two, as they're learning, they're also picking up practical knowledge like how to win king and pawn or rook and pawn endgames, as well as developing an understanding of relatively advanced chess concepts such as opposition and zugzwang!
As a third (semi) bonus, the kids I coached were always better in the endgame than their peers. This meant they could often pull a win out of a drawn or lost position, simply because they understood the endgame better than the other guy. Unfortunately this often lead to them deliberately leaving a balanced middlegame to head for a losing endgame, since they had the experience and confidence to believe they had an edge anyways. Great strategy against people who don't know endgames, and a great way to lose a lot of otherwise even games against someone who does!


I'll just sit back and wonder
Those who can ... do.
Those who can't ... teach.
Those who can't teach ... teach others to teach.