Photography is about telling a story. Start there. Think about the message you want to send, and then craft a picture around it.
Technique wise, there isn't much different about photographing a newborn that wouldn't also apply to other portraiture (much of which, in turn, applies to all photgraphy). The only things I can think of that might be different are:
- Be careful with your flash, so as to not to wake or startle your kid. Lean towards natural light whenever possible.
- "Getting in close", which is good advice, means getting in really close for your small subject. Consider getting a lens with good close-in/macro performance.
Beyond that, look for general portraitureportraiture techniques, both here and in other resources. Here's some quickies:
- Use off-axis / off-camera lighting, including natural lighting.
- Use diffuse lighting. (Especially important for newborns as it makes them look more delicate)
- Keep the eyes in focus above all else
- Use shallow depth-of-field whenever possible to bring your subject out from the background
- Try to fill the frame with face; it makes for a more interesting photo