Actually deaths weren't quite as common as one might think, though they did happen with much larger frequency. Women are, after all, BUILT to bear children, so the function isn't exactly beyond their ability.
A common practice was to prop the woman up, allowing gravity to help aid in the birthing process. Really, the way we do it now is kinda unnatural and needlessly medicated and complicated. We have way more Caesarian Sections than need be, for example.