I taught my two daughters how to play using Alburt's Comprehensive Chess Course Vol I at 5 yrs old.  Since then my younger daughter has continued playing and joined her school club.  She is now 8 and is third in her school's ladder (about 30 kids k-6), and is now playing in tournaments.  She has a 600 USCF rating, and needs help with basic piece safety and tactics.  So I created a training program for her focusing primarily on board vision, piece safety, and basic tactics.  If it works well, I'll use this same method to teach my two sons later (they are 2 and unborn!)  Here is the program, and I'd appreciate feedback from everyone (we're doing endgame stuff through Silman's course, and she has a set opening repertoire as white and black...this program is just for tactics):

1-3 times a week:

-- review the basic mates at a board (RR, Q, R, and QR -- she can do the QR ladder technique, but prefers to mate the king going down the middle of the board...she calls it "walking the dog").  I have seen too many kids draw/stalemate these won endings.

-- basic piece attacks at a board (on an empty board she places a piece anywhere she wants...I then place a pawn down and ask her to find the two squares she can move her piece to in order to attack the pawn, and she has to tell me if her piece is safe or not.  I then move the pawn around the board and ask her the same question.  Then I change the target to a king, bishop, rook, knight, queen.  This reinforces that the Bishop and Rook ALWAYS have two squares to move to in order to attack any target...queens can have up to eight -- i have also taught her that since the queen has so many options, it is easier to look at the lines out from your target to see if your queen can get onto any of them, some of which can be behind your target...for the other pieces it is easiest to just find the two squares, always in front of or next to your target, but never behind. Knights can attack any other piece on its own circle of 8 from two squares (one to the left/top of the target and one right/below the target) UNLESS the target is at the furthest point on the circle when there is only one square (or you are near the edge of the board).  It also reinforces the geometry of the movement/attacks of the pieces, and to think about piece safety on every move. She actually loves this exercise.  This is a modification of one of the techniques Heisman recommends for total beginners that we used when she was first learning.

-- heisman basic counting exercises also at a board.

-- Fritz attack/defense/check training (Fritz 13 has these awesome training features that help you see captures, loose pieces, and checks.  I use this myself daily and have seen excellent results in my own games.). Set the timer for 1 minute, repeat each 5 times and record your results.  The game is to watch your score improve over time and to compete with your own score.

-- Blitz games using fried liver, scotch and Dutch openings.  2 min games alternating black and white...as many games as she wants.  These are very tactical open games and the fried liver is extremely common U600 scholastic play.  She has an opening repertoire she really plays in tournaments as white (always 1. e4, then the Scotch against e5, and KIA against every other black response) but she needs to be able to defend against very tactical openings like these.  It also makes things more fun to play.

-- tactics training (she has one chapter left in Bain's tactics for kids, and then she will start this new program.  We will slowly go through positions in Predator at the Chess Board, aka chesstactics.org.  Some of the positions are very very complicated for her, but I really like the visual clues he teaches for each tactic --like for knight forks you look at what color your knight is on and look for targets on the same color...I wish someone had taught me THAT very simple visual clue when I was 8!!  my daughter will like the verbal explanations.  As we start a new section of the book -- I bought it to support the author! -- I will add that tactic to the custom tactics set here on Chess Tempo, which I have now set for a max rating of 1000 and includes hanging pieces, back rank mates, and forks/double attacks (chapter 1 in Predator). I'll increase the rating cap and add new tactical themes as she progresses.

The blitz games and tactical training she will do on Chess Tempo. I picked this website because of the custom tactics sets, the awesome analytics, and the ability to customize settings for blitz vs computer...all in one place.  She starts this new program soon, and since this is all a work in progress any ideas/suggestions are welcome!!

The goal is to play more games, to see more of the board, improve piece safety, get better at counting, and to understand the geometry of the pieces and their tactics.  Again I am teaching her other parts of the game separately...this is all just tactics.