Best Angle
Take shots of the subject from different angles. In this way, you'll end up with more interesting pictures. Since you are using a digicam, you won't be wasting film. Just delete those shots that you don't like and try again. the word is "EXPERIMENT".
Close Encounter
Personally I prefer to capture my subjects up close. The picture is more interesting when you manage to capture details (eg a slight dimple on a toddler's face which might not be obvious in a full body shot). Move in close to the subject or just use the zoom feature of your digicam.
Parallax Error
Keep in mind that most digicams have a viewfinder that sees the subject from a slightly different angle than the lens. This results in a parallax error. The closer you are to your subject, the greater the error. Take note of the framing marks in the viewfinder. If you keep within those boundaries, your shots should be picture perfect. Alternatively, you could always frame your subjects with the LCD screen.
Tricky LCD
If you like using the LCD, just be aware that the picture might be slightly different from what you saw on the LCD. Your picture might be brighter or darker. If you are able to adjust the LCD's brightness, don't choose the extremes. Let the brightness be balanced, in this way you reduce the chances of the pictures being too bright or too dark.
Useful Tripod
Use a tripod especially when shooting panaromic scenes or when shooting for an extended period of time. This gives you more control and stability. It also ensures the pictures taken are not blurred by shaky hands. Just make sure the tripod is on level ground. Otherwise it could topple over and smash your prized possession.