They have a few different ways but one is watching the baby with ultrasound while pushing and manipulating the baby from the outside. It’s almost unbelievable.
They manipulate the baby from the outside. Sometimes they give drugs to help relax the muscle wall of the uterus.
I think some countries are more inclined to do it. @jca2 is probably right that in America they probably opt for c-section a lot of the time, but as far as I know America does still do it. It probably depends on the doctor, the state standards of care, and what the mother prefers.
@JLeslie: I don’t think the mother’s preference comes into play when it comes to the doctor deciding whether or not to do a C-section. If the birth is liable to have complications, the mother can protest all she wants but the doctor is not going to risk the liability just because the mother doesn’t prefer an operation.