To master chess, you need more than just knowing the pieces and their moves - you need to be able to make notations of your moves. To make a short notation, write the piece name and square it moved to; for example, Bd2 for bishop on d2. Pawns don't need the piece name, just the square; e.g. g5. Show your kids how to draw lines to the board for the moves given.
Teach your child the rules of castling: no castling if the king is under attack or will move onto an attacked square, or cross an attack line. To prepare for a game of chess, help your child complete the exercise of identifying when the king can castle – check the pictures.