What can I expect to happen to my baby following delivery?

Transitional phase. A lot happens immediately after delivery. The newborn is assessed by nursing and possibly a pediatrician or neonatologist. The initial goal is to make sure that the infant transitions well from being in the womb to breathing on its own. Once the baby is thought to have transitioned well (usually after the first few minutes), the baby is often given to the mother to bond and to attempt nursing.
Hold and nurse. Right after delivery the cord will be clamped and cut, and baby will be briefly dried off (that's important to keep temperature from dropping.) then you'll get to hold baby close and warm. Soon after, it's time to nurse! Often in the delivery room baby will also get a 1st bath and a quick exam just to make sure no issues.