Get friendly with a midwife who does home births, and see if someone will let
you attend one.  When all goes well, mom helps lift baby out and onto her
tummy. The room is warm and dark, and warm towels or blankets are placed over
both to dry the baby.  The cord is left alone until it stops pulsing;
eventually the placenta slides out and the cord is cut, usually by dad. Baby
snuzzles around and gets herself onto the breast. No eye stuff for a couple
of hours; no injections yet if ever. If mom's not hemorrhaging and baby looks
good, the midwives just watch peacefully while they fill out paperwork.
 After the first nursing (1-2 hours after birth), someone cuddles the zonked
baby (and weighs & measures her) while someone else helps mom shower, tucks
them both back into bed, and sets a jug of water and plate of fruit next to
the bed. So peaceful. If you get to see this this ONCE, you'll never be the
same again.

-Linda Smith, watched my granddaughter birthed this way with amazement and
wonder after 17 years of observing hospital births.