In my case (this was a few years back when the kids were little) it was all about good budgeting. Obviously the one income has to be at least minimally sufficient to cover things. But, beyond that, it was about minimizing expenses through vigorous budgeting and frequent re-budgeting as things changed.
We never intended for my wife to stay home with the kids, but it worked at first so we just kept it going. She eventually rejoined the workforce when the kids were much older, but we made it work for a long time.