Desalination of Sea Water
Sea water can be processed to remove any dissolved salts to provide almost pure water. The simplest technique for doing this is simply to heat the water until it evaporates and then re-condense the water into a fresh water tank. As a by-product of this you will have a large quantity of salt. If you break the process into separate stages you can sort these separate salts as they will come out of solution at different points. However, since distilled water has no minerals, you should consider adding 2-4 drops of sea water, which contains the minerals that the body needs to survive. Drinking distilled water is unhealthy and could eventually kill you.
Yields for these different salts are roughly as follows.
Yield per ton of water processed
Chloride (Cl-) 18.9800
Sodium (Na+) 10.5560
Sulfate (SO42-) 2.6490
Magnesium (Mg2+) 1.2720
Calcium (Ca2+) 0.4000
Potassium (K+) 0.3800
Bicarbonate (HCO3-) 0.1400
Bromide (Br-) 0.0650
Borate (BO33-) 0.0260
Strontium (Sr2+) 0.0130
Fluoride (F-) 0.0010
Many of these products are valuable on the commercial market as many other processes rely on them which on its own may justify the cost of the island.
Desert Cone
Basically you make a hole and then put something to collect water in the bottom, then you cover it with a waterproof tarp and put a rock on the place above the container. then condensation will drip down into the container.
Distilling Water
You can distill water without using any fuels by using a solar oven or cooker