I am still building up my portfolio and at the moment, I am loving the joys of capturing children in play. They are hard work, wriggle, move around plenty (hate to sit still), smile weirdly if requested to do so, and mostly they are genuinely shy; but when you get the shot, and it may only be one after taking 100, it will be so very rewarding.
I have learnt you need to take time out to get to know the children a bit first, hang out with them, even if you do already know them or their parents, give them some attention first. Play on the swings with them, read a book if its indoors. Make them laugh and giggle so they can be comfortable in your presence.
Then let them go let them admire the ants, run around, watch other children, play with leaves, sticks or their toys and interact with their siblings or parents. They will quickly forget you're there. This lets them be themselves. Set yourself as a background prop and let them create the magic.
You just have to click the shutter.