Some thoughts, and this is from experience even though I am just a hobbyst (with just one grandaughter), and an available light shooter;
#1 Get down to their level - it will make the shots more "intimate".
#2 Know your gear backward - keep in mind that if you are not looking through the viwfinder you usually can't shoot it.
Fidling with the camera is not good or playing around with menues.
Know how to quickly and consistently nail the exposure and the focus (on the eyes).
#3 Overcast days or indirect skylight is your friend (no harsh shadows or squinting).
#4 If shooting indoors windows with indirect skylight are also your friend.
#5 Be prepared to shoot at high to very high ISO values if need be and be prepared to post process your raw files to get the most out of them.
#6 Fill the frame with your subject, however shoot a little "loose" so you are not inadverantly cutting off hands or feet etc
I generally like to use fast lenses at wider apertures (to isolate the subject) and auto ISO.
I usually shoot aperture priority with some exposure compensation dialed in if need be (my current bodies have a live histogram in the viewfinder).
When shooting I keep chimping to a minimum unless the subject wants to see the image I have just shot.
For practice you may like to try shooting birds in flight!
Some thoughts, and this is from experience even th... (