Get an Easy Chess Set
Purchase a set with pieces that are highly distinct and recognizable. A child will be forced to spend less time memorizing the pieces.
Go Over Basic Rules
Introduce children to the basic rules of the game. Set up a few pieces and go over the moves of each piece, as well as capturing enemy pieces. This isn't the time to introduce strategy into the game. Keep it simple. Likewise, feel free to leave castling and checkmate out of the game at this point. To test children's comprehension of the game, place some pieces on the board and ask them to make a move.
Use Rule Cards
Some chess sets include small rule cards the explain the possible moves of each piece, which can be helpful for new players. If these cards are used, make sure children do not become dependent on them. The idea is to get the child to remember the rules so that they can spend their time on other aspects of the game.
Play a Game of Monster
Monster is a variant of chess that takes differing skill levels into account and will enable children to learn to watch their pieces. To play a game of Monster, set up a basic chess board, but remove all but the middle five pawns and king of the more skilled player. Children will appreciate not having to worry about long-ranged pieces attacking them, and are more free to concentrate on making proper moves. Focus on helping the child make proper moves and understand how the board is laid out during a game. Don't worry about checkmate.
Take it Easy and Communicate
Chess is about fun for both players, so remember not to take it too seriously with a child. Many children will love the opportunity to try the game, but might become frustrated if they continue to lose badly all the time. As the teacher, make moves that create opportunities for children to show their prowess in the game, and allow the child to taste victory occasionally. Keep communicating with the child, even if it means giving away your dazzling plans at checkmate, and ask the child to tell you about what they are thinking. This might identify some places where additional instruction would be helpful.