This is our very basic overview.

Part 3: Third Stage--Newborn Procedures
Immediately after birth, they may place the baby up on mom's belly, or may take it over to a warming table, depending on the condition of the baby and on hospital policy. The doctor will deliver the placenta: you may need to do a few more light pushes. Then the doctor will examine your perineum, and will repair any tears or episiotomy.

Hospital policies vary regarding immediate newborn care, but most hospitals in the Seattle area will attempt to leave the baby in its parents' arms for as much of the first hour as possible, to allow for initial bonding, and the first breastfeeding. At the end of one hour, some mandatory procedures are done with the infant, including antibiotic eye ointment, and a Vitamin K shot. Typically, the baby is also weighed and measured at this time, and may be given its first bath.