Distillation will remove microbes, heavy metals, salts, most chemicals, and radioactive fallout. It is the only method that can purify salt water.
“Distillation involves boiling water and collecting the vapor. The vapor condenses back to water but will not include salt and other impurities. To distill, use a clean pot with a lid that will stay in place and cover the pot when placed upside down on the top. The lid needs to have a handle in the center, or near-center, top. Fill the clean pot halfway with water. Tie a clean cup to the handle on the pot’s lid so that the cup will hang right-side-up when the lid is upside-down. The cup should hang suspended above the water, not dangle into the water. Boil the water for 20 minutes. The water that drips from the lid into the cup is distilled.”1
Equipment specifically manufactured for emergency water distillation at home can be purchased from several companies.
1The University of Georgia Cooperative Extension “Preparing an Emergency Food Supply, Storing Water Supplies”