Daddy's Tips for Better Photography
Know Basic Principles of Photography - shutter speed, lens aperature, "film" speed, exposure, focus, backlighting, flash distance - and how each affects picture.
If the light is behind them (in front of a window) or on a sunny day under a tree with shadows and sun moving about their face.
Solution: In both cases, use the flash to brighten the faces.
Get close, or use the zoom. Fill the picture with their face.
Ask them to do something funny, or make a funny face
Blur the background (large lens opening needed)
Make sure the background is plain so it doesn't distract from the person.
Take a look at the pictures in National Geographic Magazine. Pictures don't get better than these!
Use a small lens opening so you can get objects close to you and far away from you in focus
Move around - try several angles
I learned about photography from Kodak's Guide to 35 mm Photography. It's still in my library.
On-Line Guides to Taking Better Photographs
BBC Advanced Photography Tips