Chess For Kids

I completely encourage children learning chess, it's a fun game that teaches practical skills such as pattern recognition, competition, patience, and other virtues.

The method I use

When I am going to teach someone chess, I teach piece by piece, starting with just pawns. After teaching how the pawns can move, and a few basic 3vs3 1vs2 scenarios, setup the pawns on their starting positions. The object of the game is to advance a single pawn to the 8th rank. That's it! Play this around 50 times (not in a single sitting of course), the more the better. This will familiarize the budding Kasparov with how the pawns interact, aid each other, and move in general.

After this add a single piece, a knight for each side in addition to the pawns. The idea here is that each piece can aid the pawns in their own way so we have to learn how each piece individually can help the team. Continue adding a single piece, and removing it, just knight, just bishop, just rook and pawns and so forth for all pieces. Then go back and play with 2 knights/bishops/rooks and the pawns. Keep progressing until the player is completely familiar with all the piece combinations, without being bogged down with opening theory, or tactical traps.

Using this method, my first student went 15 moves into the Queen's Gambit Declined in their very first complete game.

After the player has a good command of moving the pieces, and desires to progress, there are plenty of great books to elevate the new chess player's strength

Tactics

This is my favorite "starter" book.
Bobby Fisher Teaches Chess
A great idea for a book, and well put together with the top mating combinations
How to Beat Your Dad at Chess

Openings

Chess Openings Traps and Zaps: Bruce Pandolfini