Echoing what the ladies have said above Mollie. Also don't turn all of the house lights on trying to get more light, ugly ugly things happen then! FInd nice light filtering in from a window. The first week is such a perfect time too. Right after the baby is fed is perfect timing to be able to manipulate him/her for shots. Get down on the level of the baby and do some from a straight on angle.
Definitely use AV mode and keep your shutter speed above 1/50.
Hopefully Kim will chime in here since she's the baby expert
