Every element can exist in three states: as a liquid, as a solid and as a vapor, mostly depending on its temperature. This applies to water, too. So, water can be found as ice, water and steam. If water is cooled down below 0 degrees Celsius (32 Fahrenheit), it becomes ice, and if heated above 100 degrees Celsius (212 Fahrenheit), it becomes steam. The temperature, at which a substance changes it state from liquid to vapor is called a boiling point, and it is different for different substances. This difference can be used to separate substances, and as such can be used for water purification.
You can easily come up with your own solution for distilling water once you understand what distilling involves. There are three major steps to distilling water. Also some minor ones like cleanliness of equipment and having connections as airtight as possible, but I think that most of them are common sense. All distilling consists of is evaporating water then cooling the evaporated water and collecting the clean, pure water. Almost anything will work in a pinch. Distillation is a simple process. Don't forget that dew is essentially distilled water. If you can recreate the dewing process and collect the water from it then you are also on your way to clean water.
I have read survival books that say that a clean piece of cloth over a boiling pot can be sucked on or wrung out in the most desperate situations. Not very effective, but you get the point. I have seen something that takes a curved glass lid oversized for its container that allows light in and catches the water as it evaporates and drops it over the edge of the original water container. I've seen a diagram for a campfire distiller that uses the campfire to heat the water, runs a tube underground to cool and condense the water and then collects it in a half buried container to minimize evaporation from the secondary container.
Offered by John.