Let's face it, most kids really couldn't care less about having their picture taken. Chances are they'd rather be playing something way more fun than "camera studio" or whatever other kind of nonsense we feed them to get them to actually be within the frame of our camera.
I've learned through much trial and error that there are certain things you will just not convince a child of by explaining that "mommy wants a good picture of you" or "grandma and grandpa are going to have this hanging on their wall". Child photography is mostly about being quick and secondly about playing the psychology game with kids to make it fun for them and not a chore.
Some things that (usually) work for me...
1. Get them involved.
One of the things that I find extremely helpful when photographing children is to get them involved in the process. Plunking them exactly where you want them and saying, "now smile naturally" just doesn't work. No really. I'm serious. It doesn't.
It's far easier to get a natural picture of a child if you let them explore the setting that you want to have them in and if there's something of interest to them within the setting of your shot.
2. Location, location, location.
Obviously a child is going to be much more keen to get their picture taken when they're also having fun. Taking a child to the beach, or a park, or a bridge over a creek can create an awesome background and also pique their curiousity allowing them to walk and investigate while you're snapping frantically.
3. Be quick!
Kids are movers and unless you can work some kind of serious magic your subject ain't gonna sit still for long! Remember that your shutter button is your friend and it likes to be pushed often. Kids also tend to make silly faces when a camera is pointed at their face so it's imperative that you shoot lots in order to get those few stellar shots of children.
4. Be patient.
Chances are you won't be able to get the shot you want straight off the bat. Give the child time to warm up to you and their surroundings. Give them some space, sit back and watch, but always be ready!
5. Choose your equipment wisely.
There's no need for a tripod when you're photographing children. It will likely just cause you much frustration as child subjects are constantly on the move. You'll want to hand hold your camera so you can move with the child and get right up close. I would also recommend using a farily high ISO film because again, your subject won't be able to sit still for long. Also, be sure to have your equipment fully prepared before you even meet with the child. They'll get seriously bored with you if you're spending your time together changing batteries, lenses, and cleaning equipment.
6. Shoot at eye level.
Getting down to a child's level will not only make them feel more comfortable with you but eye-to-eye contact is also extremely engaging in a photo. The expressions you capture from the child's perspective will look much more natural than if you're hovering above them.
7. Get close!
Once the child is comfortable with you and your camera try and get in a little bit closer. It isn't necessary to have the child's full body in every shot. Often times the sweetest, most intimate shots come from focusing on the child's face and capturing expressions that are unique and natural to them.
8. Finish on a good note.
Likely, the child will be DONE by the time you've got the shots you're after. Instead of sending a child away from a session tired and grumpy, finish it on a high note for them.
One thing I like to do is allow the child to take one picture before they're off. Hold the camera for them as they look through the viewfinder and guide them to pushing the right button. If you're shooting digitally they can see the results immediately and they'll go away from your session excited and looking forward to coming back so they can, "do that again!"