When photographing children yourself, professionals advise:
Use available light when possible, or soft studio lights which won't make a child uncomfortable.
Don't make the child pose or perform.
Let the child become used to you with a camera before you actually start taking pictures.
If you're using color film, don't dress the child in bright colors such as reds, oranges, and yellows, or prints and checks which will distract from the child's face.
When using a 35mm camera, use fast shutter speeds to avoid blurring (1/100 or faster) and small lens openings for depth of field (f/8 to f/16).
Their advice, when going to a professional:
Talk to the photographer ahead of time, alone, about what type of photograph you want, about the child's personality, and about the type of clothes the child should wear.
Trust the photographer to know how to handle your child instead of "butting in" when not asked.
Don't talk too much to the child about the photo session ahead of time -- let it be a new experience.
Order duplicates of photos taken, one for yourself and one for the child when he is grown.
If you are thinking of having a picture taken for Christmas presents, don't wait until the last minute to make an appointment.