They are peeled, crushed, their juice extracted (the solid parts became cattle fodder), squeezed, boiled down, and the water evaporated until dry 'crystals' are left. The crystal form of the sugar is...
You first wash the cane/sugar beet. Then you crush them to get as much juice out as possible. This juice contains a lot of sugar, but at this stage there is also a lot of water (hence why it is juice...