Researchers at MIT and China have developed old-fashioned solar steel using a new inexpensive device that uses the sun to remove salt from water. Traditionally, this type of system uses a lamp to draw water, but once the lamp is fouled with salt, the device needs cleaning or other maintenance. Survival is not exactly what you want. If you want more details you can read the paper in nature.
The key to this new technique is black paint and polyurethane with 2.5-millimeter perforations. The idea is that warm water above the insulation medium condenses the salt into the cold water below the insulation which allows efficient evaporation of water. As the water evaporates, it increases the concentration of salt at the top, which then sinks due to the higher concentration, and the lower density salt rises to the top to evaporate the water.
Since the materials are generic, the team says the one-meter-square system costs about $ 4 to produce. A system that can provide daily drinking water to a household of that size.
So far, the prototype system has been working in the lab for at least a week without salt. The next challenge is to scale it to something more practical, but because of the low cost and simplicity of the system, it looks like it will be easy enough to do or reproduce the device for your own testing.
Purification is a problem that you can approach from different angles. You can also collect clean water from the fog, something else that started at MIT.