Lenses
As with any portrait, using a wide-angle lens is highly discouraged because distortion of features will occur, particularly when the photographer is close to the child. Using a "normal" lens (35 to 50 mm depending on the size of your digital camera's sensor) is recommended for making a three-quarter or full-length portrait. For head and shoulders and facial portraits, try using a long lens farther away from the child, which naturally creates a more shallow depth of field, blurring the background.
Focusing
Children can be difficult subjects to keep in focus for obvious reasons. If you're dealing with a toddler, a camera with multipoint auto focus and/or predictive auto focus is very helpful. The first will allow you to keep the lens focused on areas other than the center, inspiring more creative compositions. The second actually predicts movement and changes focus according to the moving child. Make sure the child's eyes are in focus, and get to know your lens so you become familiar with how much of the rest of his face will fall into focus depending on your chosen aperture.
Lighting
Children will feel more comfortable outdoors in natural lighting, if such a shoot is possible. Avoid the light of a sunny day at noon, as it creates unattractive shadows in the eye sockets and harsh contrast. If you are using a studio lighting setup, good lighting ratios for children fall between 2 to 1 and 3.5 to 1. Higher ratios create greater contrast, which narrows the cherub-like roundness of their faces.
Interaction
You will get much better results with your photos if you have a sense of how to interact with the children based on their age. Newborns are best to photograph immediately after a feeding. Babies dislike being separated from mom, so consider compositions that can be made whilst being held. Around seven months is a good age to photograph, as babies are social but not yet fully mobile. For 2 year olds, don't have a lot of expectations or a tight backdrop; hand-hold the camera and follow them. Older kids can be spoken to, but never ask a child to smile. Instead, create a smile by giving her toys to play with or asking silly questions.
Composition
Children who aren't mobile present challenges to dynamic compositions, as it is difficult to work with angling of their heads and shoulders. Creative camera angles can assist with this. For a head and shoulders portrait, however, bring the point of view directly to the nose. Being above the nose can narrow the cheeks and chin, while below can distort the shape of the head. If the child is older, you can use her activity to your advantage. Try using a relatively slow shutter speed, such as 1/60 of a second, to blur the motion of a spinning or jumping child for a creative effect.