How do I devise a method to obtain pure water from seawater.

The technology does exist.
The process is called REVERSE OSMOSIS.
These plants are usually large and are
Installed by Governments.
They exist in many countries.
Malta has made great use of such plants.

Reverse osmosis. Chemists use a process called reverse osmosis to purify water and perform other functions. In normal osmosis, water flows from fresh water into seawater when they are separated by an appropriate semipermeable membrane. But, by applying pressure to the seawater, chemists can reverse the movement of the water and produce fresh water from seawater. Some shipwreck victims have used survival kits that convert seawater into drinking water by osmosis .

Contributor: John B. Butt, D.Eng. Walter P. Murphy Prof. of Chemical Engineering, Northwestern Univ.

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85% of the world's desalination is performed through Multi-stage Flash Distillation. This is an alternative to reverse osmosis.

Multi-stage flash distillation - Wikipedia, the free encyclopedia