Learning chess can be easy and fun! Teaching chess to children or other adults can also be very easy. Although this article does not describe the only way to teach chess, it is an effective way I have used for over 30 years of chess coaching at many levels.
Start slow! Teach them one "easy-to-learn" concept, and then add-to-that by building up gradually to more complex positions and concepts using various aspects from the first concept you taught. Parents can, without knowing a lot of chess theory or ideas, easily ask questions of their children, and then simply listen to their answers. Buying them a beginner level chess book is good, because if they are interested in chess, they will soon dig deeply into it.
Once the child is engrossed in the chess book, all a parent has to do is ask: "What did you learn today by studying?", and "will you teach me that idea”? Then the parent takes the ‘defending’ side, and struggles in various ways to try and draw, or win the position against the child or student. The student, who has explained the ‘theory’ of the position, now has to repeatedly prove that they really did understand the ideas, and that they can apply the principles of the position to ‘win’ it.
Once they learn the basics of how each piece can move, they need to learn chess ‘notation’. Chess notation is a method of writing the moves on a sheet of paper, so as to enable someone who did not see the game in person to recreate the moves and follow the concepts involved in the game. Next they are ready to learn patterns, techniques, and strategies to help them win chess games. You can find the 'basics' of chess, in both how to move the pieces and beginning strategies at this URL: http://www.chess.com/learn-how-to-play-chess.html
Now it is time for you to try the teaching methods I have described above by teaching one strategy/technique that is critical to chess improvement: "Opposition". What is opposition? Basically, Opposition is a battle for square control between the opposing kings! Vertical or horizontal Opposition involves the two Kings facing off against each other in close range, with only one square between them.
Knowing this technique and pattern is important for many stages of chess, so here are a few links to articles written by other ChessKid.com contributers to help you learn several ways of using this tool!
Learn more about King vs King Opposition, in terms of how to win, from this article by GracefulLady!
Learn more about King and Rook Checkmate, using Opposition, from this article by Bounding Owl!
Try to use the methods above to help your child truly integrate these important ideas! Good luck!!!