NOTE: If you try this with water from your kitchen sink, the filtered or distilled water will very likely be good to drink. However, if you try this with murky lake or pond water, I don't recommend drinking it after only one filtration or distillation!! Sometimes water can hold dangerous viruses that a filter will not remove, and some of the dirty water could splash during distillation, putting some microorganisms in your clean water.
We found a great website that shows how to make a filter that uses cotton, gravel and sand, and an empty plastic water bottle. Please visit Instructables.com to see how they made their simple water filter. This one would be very good for a school project!
We also tried making a water distillation system ourselves using a pot of boiling water on a stove, a large pot lid, a bowl, and a bag of ice. You assemble the system as in the figure below:
We tried this, and it worked well! Please watch our YouTube video and see!