Just this past evening (12/13/2010) I had the opportunity to photograph Destiny Polles. I think she is 6 days old here. Over all I didn't get to take that many photographs because well Destiny runs the show. Everyone in the house is her time table and she was not overly happy about the photographer that had invaded her nap time. Honestly, with a subject like this taking a bad photo was much harder than taking a good one.
There are a few things to remember when photographing a newborn.
You are on their time table and they control the shoot. Period.
You must have patience and be ready for that fleeting expression.
This is a human being, albeit a small one, and as such should be treated with respect and understanding. Their comfort and sense of security should remain vitally important to you as a photographer. If that means coming back another day when they are more willing to accept your presence then fine.
Soft lighting is your friend. Use umbrellas or softboxes to ensure even soft light. If you want to go for an edgy look then you can remove the umbrella or softbox and shoot away. However, that is not necessarily something you should do for every shot as it is not overly flattering.
Remain as calm and quiet as you can so as not to put the subject on edge.
Remember to have fun! Your attitude can have a great effect on the parents and the baby. The more relaxed all parties involved feel the better the shoot will be.