Distillation - involves boiling the water to produce water vapour. The vapour contacts a cool surface where it condenses as a liquid. Because the solutes are not normally vaporised, they remain in the boiling solution. Even distillation does not completely purify water, because of contaminants with similar boiling points and droplets of unvaporised liquid carried with the steam. However, 99.9% pure water can be obtained by distillation. then you use electrodeionization to purify it further... Water is passed between a positive electrode and a negative electrode. Ion selective membranes allow the positive ions to separate from the water toward the negative electrode and the negative ions toward the positive electrode. High purity deionized water results. The water is usually passed through a reverse osmosis unit first to remove non-ionic organic contaminants. the first method is ez.. just use fire lol.. not much energy wasted there. the second step would be a bit more complex, but you'd have solid drinking water in the end... as long as the earth is like 80% covered in H2O we're fine
^ Fire uses energy, and when you are talking about multiple thousand metric tonnes worth of water? Purification is as expensive as buying water... IF water's for sale at that point...