Basically just watch any mammalian birth, unhandled by veterinarians, and that should give a good idea. I'm not at that stage of my life so I haven't done any extensive research on it, but the umbilical cord falls off eventually when the body deems the baby ready, and the placenta falls out of the mother around when the baby disconnects. I've heard some people eat the placenta, I'm not sure how that works if it tastes good etc. just heard that's a thing. You might want a midwife who has some experience with other births, experience is always good because there can be complications like breech position which are easily solved from hands on experience. Try to find one that is as natural as possible. With how unhealthy everyone is nowadays, it's more likely that things don't go as smoothly as they would pre-industrially. Make sure your wife is drinking filtered water but getting all the minerals she needs, which the filter may take out. Fluoride wreaks a similar amount of damage as clamping, prenatally continuing throughout childhood.
I wish you many unclamped white children and no defects.