This is a real specialty of mine. I'm the referred photographer for several agencies that exclusively handle young performers. I'm also the dad to an 13 and a 6 year old... I've been around kids a lot.
The younger the child, the harder it is to get them to sit still, so, generally I shoot fast and generously - I take a lot of pictures. Invariable I get a good one this way.
Younger kids also melt down more quickly than older kids - you might only get 10 or 20 minutes of shooting before they get unworkable, so speed and a sense of humor with children are the key.
Like teenagers, kids should look their age and not like stiff small adults. And in terms of casting, it is better for kids to look younger rather than older.