Giving birth can be traumatic, and hormones continue to ebb and flow after childbirth. If there is ever a time to be understanding of your baby's mom, and available to her, too, this is it. Try not to schedule too many things in one day. Everything takes longer with a baby involved. If you have a medical question about your baby, call your pediatrician, but don't panic.
Babies are sturdier than they look.
Talk to other new fathers about your experience and theirs. Mothers' groups abound, and women love them. You don't need to call it a men's group, and you don't have to hug. Take care of yourself. Keep an eye on your driving, your diet, and your risk-taking.