Well i am not Dan, but I wil jump in:) two basic methods would be a centrifuge and vacume distillation.
Water in the oil will naturally separate over time, just set a WVO sample on a shelf undisturbed for a few months and see what happens. A bit of heat will accelerate this process as the separation occurs easier with warmer oil. A centrifuge speeds up this process by applying several thousand "G"s(2000-4000) to the oil in a spinning bowl or basin. The bowl has a top lip which contains the oil that is slung out to the sides of the spinning bowl. As more oil is added the level eventually reaches a point where it flows over this lip to be slung against the outer case. The contaminated oil is added to the bottom of the bowl where it is accelerated outward and the tremendous G force is applied. This separates the heavier elements/particles and of course water is heavier than oil so it travels to the outside of the spinning bowl. The oil slowly travels from the bottom to the top, shedding it's heavier contaminants outward untill it reaches the bowl lip and is slung off the bowl to be recovered. Again, heat also helps with this process. The bowl must be stopped from time to time to clean out the water and separated contaminants lest they fill the bowl to the lip and spill over along with the cleaner oil. There are self cleaning units such as those made by Alfl-Laval but they are fairly complex and very expensive. Check out the videos section at
www.simplecentrifuge.com. They have a pretty good animation that shows how the process works.
Water boils at different temperatures based on the pressure. The lower the pressure, the lower the boiling point. If you apply enough vacume to a sample of WVO, you could in theory boil the water out of the oil at room temperature. Typically a lesser vacume and some moderate heat is applied to cause the separation. The water turns to steam/vapor and must be drawn out of the chamber. This is done by circulating air(under the same vacume) thru the chamber top to a dessicant filter to absorb the moisture or to a condenser where it is cooled and the water can reform outside the oil chamber. This dried air is then returned to the chamber to pickup more water vapor. Agitation of the oil helps to get the vaporised water out of the oil. Depending on the vacume and temp used and the ammount of water in the oil, the boiling process could also be quite violent, but far safer than doing it at atmospheric pressure and 212 degrees F.
There are companies that specialize in doing this to installed hydraulic systems where the working temp of the oil in use provides enough heat to boil off the water under vacume.
If I recall the freshwater evaps I used to work with, the first stage was under 17" of vacume and boiled at 133 degrees F. We recovered enough heat from the distilled freshwater in the first stage to boil the sea water in the second stage under about 24" of vacume(forget the temp).
Ron