One thing to remember is to teach bit by bit. You build on your teaching. You start with one thing, then add to it once the child has that one thing down. A simple example of this is teaching moral actions to children. First, you teach to share. Then as the child is able, you start to teach simple reasons why they do these moral actions. As they continue to grow, you add to that. It is the idea of "milk before meat" or "line upon line and precept on precept."
Also keep in mind that you are teaching "people, not lessons." You might think out a plan of what needs to be taught at a certain time. When it comes time to teach that, however, you might find the teaching naturally leads in a different direction, or perhaps it doesn't cover all you wanted to cover. That is okay. Teach the individual and that individual will learn more from it.
Along the same lines, as you are teaching, stop to observe the child and carefully consider what to do next. Silence is okay. You can think for a moment before proceeding. This is true of teaching, disciplining, or even just having a nice conversation. You can think before you speak.
You want to teach your children to value, not just about values. It is one thing to talk about the right actions and another to put these actions into action in the real world. Teaching to serve is nice, but being a family that serves others teaches the value of service far more than talking about it does. If you are teaching morals to your child because you think that moral is important, you want to help your child to learn to live that moral--not just all of the right answers as to why it is a good idea to live that moral.
These are very simple, but effective. As you teach to the child's level and just bit by bit, teach to the individual child, take the time to think and discern while teaching, and put emphasis on living the teachings rather than knowing the teachings, you will help your child grow in his understanding of morals and the values you are trying to teach. Your child will learn to live by the principles, and that, after all, is the point in teaching them.
Ideas for this post taken from "Teaching after the Manner of the Spirit"