Newborns should, ideally, be photographed within the first two weeks after birth. A bit later is fine, but they will become more difficult to pose.
It is important to keep your house (or at least the room where the session takes place) very warm. Most newborns are posed naked, and so you need to be sure that the room is set for their comfort. So wear a tank top and crank up your heat!
Don't worry about pee and poop. Chances are that if your photographer has photographed newborns before, they've seen it all (especially if they have children themselves!).
Don't worry too much about your appearance. Life with a newborn is tough. If you plan to be in the photograph, keep it simple.
If you are doing a session at your house (my newborn sessions are on location at your home), expect to have space for a small setup. I like to have room for a small backdrop stand, lights (especially if the house is dark with no good windows), a bean bag, and various props and other tools of the trade.
Feed the baby after the photographer arrives, with a diaper covering the baby, but not with the tabs on (this will make it easier to take the diaper off later!).
Be sure to work with a photographer you trust. Ask about their safety practices, make sure you are comfortable with what they have to say. Once you have a trustworthy photographer whose style you like, enjoy, ask questions, and watch the magic happen!