Newborn & Immediate Postpartum
The resources here list the standard procedures for your newborn in the immediate postpartum.
Newborn Things
The standard of care for newborns in the hospital is to apply antibiotic eye ointment to the baby's eyes, to give an injection of Vitamin K, to give a Hepatitis B vaccine, and to take a heel-prick blood sample, often called the "PKU Test." Depending on your provider, these may or may not be presented as optional in the hospital; they are typically strongly encouraged. At home, all are optional.
Eye Ointment
Erythromycin is antibiotic eye ointment applied to the baby's eyes to prevent a type of conjunctivitis that can lead to blindness. This type of conjunctivitis can occur if the birthing parent has a chlamydia or gonorrhea infection. If a baby does have this type of eye infection, they will require further treatment. Learn more at Evidenced Based Birth.
Vitamin K
Supplemental Vitamin K is given because babies are born without it, and levels build up within the first week or so of life. Rarely, babies have a clotting disorder called Vitamin K Deficiency Bleeding (VKBD), which can be very dangerous. Supplementing with Vitamin K practically eliminates poor outcomes for those babies, but there is no way to know which babies have VKBD and which don't, so babies born in the hospital are universally treated with an injection of Vitamin K.
An alternative to the injection are Vitamin K drops; these are not offered in U.S. hospitals, but are the standard of care in some other countries. If you're unsure which approach you want to take (including whether or not to supplement at all), I encourage you to do some research. For those birthing with me at home, I can administer the injection, or you can purchase Vitamin K drops, or choose not to give supplemental Vitamin K. You can also decline the injection in the hospital, but you may take some flack from your provider for doing so.
One place to start is Evidence Based Birth
This article (PDF) from Birth Matters goes into detail on Vitamin K for out of hospital births.
Hepatitis B Vaccine
The Hepatitis B vaccine is given before you leave the hospital. I do not administer this vaccine at home. The Hepatitis B vaccine can prevent vertical transmission from an infected mother; otherwise, there is no rush to give it. Risk factors for your child contracting Hepatitis B include unsafe sexual practices and needle-sharing. If you want your child to receive the Hep B vaccine but don't want it given right after birth, it can be done by your pediatrician.
Newborn Screening
The “PKU Test” is a heel-prick blood test performed between 24-48 hours postpartum. The blood is tested for about thirty different metabolic disorders that, if identified early, are treatable. For more information, see the New England Screening Program.