On the PC, I found 2 great chess training programs for kids: Dinosaur Chess and Fritz&Chesster. The criteria was
1) It had to be a training program
2) It had to be appropriate for 4-8 yr olds
3) It had to give kids the basics (how piece move)
As of 2011, only Dinosaur Chess has been ported to the iPad. Dinosaur Chess will teach how all the pieces move, castle, check, checkmate, and stalemate. As a chess coach, I know how to do this one on one. With my daughter, I found she accepted correction by the computer easier than the correction by dad. The computer patiently corrects the child whether it be 1 or a 100 times, and the only way to get to the next level is to get the answer correct (especially important for those children that love a good test of wills). In addition, the computer makes it fun, and if you want your child to play, that's an extremely important component to learning.
In addition to teaching the rules, it has 6 different levels of play, starting with one side having 4 pawns and a King against 8 pawns and a King and working up to a full board. By reducing the pieces on the board (initially), it works a child towards checkmate, which is VERY important when teaching a child the game. Overall a great chess tutorial for kids.