[40 Deluxe]

woodypecker, It's based on the fact that water and gasoline do not mix, while water and ethanol (alcohol) mix easily and stay mixed. What you do is get a clear container (like the five gallon jugs motorcycle guys often use). Fill it 1/4 full of water and 3/4 gasoline. Shake it up good and let sit for a few hours or longer. Since water is heavier than gasoline and does not mix with gasoline, it will settle to the bottom of the jug. Since the ethanol combined with the water when we shook the jug, it goes to the bottom with the water, leaving pure gasoline on top of the water. Next you siphon the pure gas into another container and add to your car, mower, chainsaw, etc. Or you can get fancy and add a spigot to the bottom of the jug to drain off the water/ethanol slurry.
One point to remember; refineries use a low octane gasoline to blend with ethanol and count on the higher octane of the ethanol to bring the final product up to 87 or whatever octane. If you want to end up with 87 octane pure gasoline, you have to buy 91 or 92 octane premium gasohol and remove the ethanol.
Interestingly, ethanol is not added to the gasoline until the gasoline arrives at the tank terminals where the tankers pick it up to deliver to your local station. Ethanol cannot be sent through pipelines because it will absorb the water that is in all pipelines to some extent. So any gasoline you buy has already been exposed to water before you add some water to remove the ethanol.