Here are a few things you can tell them:

1. Move in closer. You don't want to get so close that the flash washes out the faces, so if the camera has a zoom feature, use it. Try to avoid long shots where the subject is lost in the middle of everything else.

2. Watch your backgrounds. This is hard to do at a party, where the background is likely to be filled with other people. But they can make sure a post (or plant) isn't sticking out of someone's head, for example.

3. If the party is during the day, be careful shooting near windows. If the subject is standing in front of a window, the camera will probably read the window light and badly underexpose the subject. You can try focusing on the subject's knees (assuming the knees are below the window), and, continuing to hold the shutter down halfway, bring the camera up to where you want it and then take the picture.

4. Stand still. Kids tend to move around a lot. This is fine as long as they're not trying to take a picture.