Enroll your child in some improvisation classes. These will help take away any stage fright she might have and teach her to be extremely creative on the fly. Improv skills will also bring out her personality even more and make her realize it's okay to let go of all inhibition, which is important in acting.
Scene study classes teach how to break down a script and understand what is really being said. Commercial classes teach how to act on camera so your child knows what colors look best on camera, understand how her angles look on camera, how to slate (state her name and age) and how to make a good impression. Between scene study and commercial classes, your child will be exposed to a crash course of acting.
To reach an emotional level, instruct your child to think back on an old memory. For instance, if he is supposed to be sad have him think about the time his grandpa or a pet died or something tragic happened. Connect those thoughts to a specific line in the script, so when he gets to that line, he starts thinking back on that memory. This is called sense memory.
Acting is all about reacting, so read the script with your child. Have her react to what you say as the other character instead of just reading her next line. Each line should be a reaction to what was just said or done. It's supposed to be spontaneous and instinctual, so work with her on creating a genuine reaction each time she rehearses a script. It will seem likes it's happening for the first time. To reach those emotional highs and lows, go through the script and talk about what's going on. Then, help her think of things to think back on for each emotion. If need be, write a little note on the side of the script to remind her (and you) of what she is supposed to be connecting to.
Practice makes perfect. Practice these techniques with your child over and over again so it becomes more natural and a habit instead of true work.