What kind of camera do you have (brand/type)? I have a Sony a230.
I've been trying to learn how to take moving pictures of them too. I figured out that you can use the Apeture button, it helps focus on the subject better. It can be harder to take a close up if your hands are shaky, so you could try using a camera stand.....though I don't know if that is a problem for you....
Try taking the picture in natural light too, if you don't already use a fluorescent bulb.
It took me a while to get a good pic in motion.