first of all, turn off your flash! there's really no substitute for natural light and a stock flash is about as bad as it gets. yes, a flash will light up your subject enough to focus on it, but if you're photographing a person, it is way too harsh of a light.
i always prefer to do outdoor shoots, but if you're working with a newborn, that's probably not practical. in this scenario, you should choose the best lit room in your house, the one with the most direct sunlight, and set up your backdrop there. also, remember that whatever you lay the baby on will be reflective in a way (unless you use a black fabric). that means that if you lay the baby on a red blanket, the light is going to get reflected onto the baby in a way the makes him/her look more red. i prefer to lay them on white, because it doesn't add a color, just brightens them up a bit.
timing is everything! when shooting indoors, you'll want to schedule the shoot for midday or the time of day when the sunlight streams into that room the most. shooting outdoors is a whole different ballgame, though.
when shooting outdoors, you have 3 options for the best light: 1) in the shade 2) on a cloudy day 3) sunrise/sunset. the main point here is to avoid the midday sun. the reason being that it casts unflattering shadows on your subjects' faces. it tends to make eyes look hooded with circles underneath. not to mention the fact that everyone would be squinting. yeah, not at all flattering.
so, back to the good options...
if you must shoot midday, try to find a nice shaded area, maybe under a tree or, if you're in a city, in an alley, etc.
|in the shade|
if the day of your shoot doesn't dawn bright and sunny, don't fret! clouds are our friends! :) i've done some of my best work on cloudy days.
|on a cloudy day|
my favorite time of day to shoot is an hour or two before sunset (an hour or two after sunrise is also a great time, but who wants to get up that early???). the light then is so soft and warm that can be very forgiving. it tends to make skin look smoother and can even soften wrinkles. try not to shoot with the sun directly in your subject's eyes, though. it's better to have the sun streaming down on them at an angle.
|side-lit at sunset|
|backlit at sunset|
also, if you have any specific questions about photography that you'd like me to cover, you can either leave me a comment or send me an email. :)