Always, take a burst of at least 3 photographs. One taken closely to the next will change the photograph quite considerably. Also, shooting in bursts of 3 or 4 shots will allow you to put the photographs together in a series.
Ensure you clean up your background material. Since the best photographs you’ll take of your children are likely going to be candid shots, you will run into the problem of having distracting backgrounds. If taking photographs of the children playing in the house, make sure to clean up the room first of all highly coloured and distracting items. When taking photographs of the children playing in the local park, change your angle to get any litter rubbish out of the background.
Child photography allows for close-up portraits as well as the child engaged in some activity. Taking the child's socks off, the child in a large box surrounded with toys or climbing on or out of something. As you continue to gain experience in working with children of various ages you will become more adept at learning what typically works with different age groups.