Before I give some specific tips on how to take photos of kids from my own experience, I think it’s worth saying that you want to get the kid that you are photographing as comfortable with you and the camera as possible.
Set the child at ease by spending time with them before taking their shots. Give out candies or toys and play with them for a while. The more relaxed they are the better. Also show kids their photos after you’ve taken them, they will love it.