How could a woman concieve with one ovary and one uterine tube which are on opposite sides?

Poor chance: The odds are not likely but it is possible and it does occur. The fallopian tubes attract the egg to it. So an egg from one side can pass behind the uterus and get picked up by the opposite tube. This is true if the tubes are anatomically low in the pelvis. Imagine passing a ball from your right hand to the left behind your back.

It can happen: Apparently, the fallopian tube is able to pick up an egg from the ovary located on the opposite side. It is probably not as efficient process as it may be when the ovary is on the same side and the tube must be of sufficient length to be in the physical proximity to the ovary.