Note: This was a writeup following a reprint of (obviously copyrighted) material from the The Worst-Case Scenario Survival Handbook. My writeup therefore does not stand out so well by itself ... hmm ... maybe one day ...
If the baby's head has not already completely come out but is just visible at the cervix (this is "crowning"), it is worthwhile putting a hand in and feeling around the baby's head to see if the umbilical cord is wrapped around its neck. If it is, take a moment to try and untwist it over the baby's head so that the bady does not get strangulated by its own umbilical cord as it is delivered.
After the baby is out, it is of paramount importance, after the baby has started breathing, that you keep the baby warm. Babies have a much higher surface area to volume ratio than adults so they lose heat quickly. In a pinch, this can be done by having the mother cuddle the dried baby.
God help you if you have a placenta praevia baby in the back of a taxi ... or any of the other obstetric emergencies. If in doubt, get the mother to a hospital immediately.
If (God forbid) an extremely unfortunate situation arises, attempt to save the mother's life first. If the mother is already dead, attempt to save the baby - perform an unsterile caesarean section if necessary.