The first advice I give to persons who want to improve their pictures of their children or grandchildren is: find the flash control and turn it off. Flash gives you a very flat picture and destroys interesting light patterns as well as rendering the background too dark. Natural light will make a much more interesting photograph. It will appear true and real as the actual situation.
However, be aware that making the picture without flash requires that you hold the camera absolutely still. You achieve this by tucking your arms against you body as you are making the photo. Also, you will need to make multiple exposures (click the shutter several times for the same scene). If you are indoors with minimal light some of the exposures may show blurred action (because the flash is not stopping the movement). If you have several exposures you will find one that is sharp. Keep that one and delete the others. These actions do not come naturally so you will need to practice them before you are with the children. Read more