Making Distilled Water
The method and information here was interesting. I like the point they make that distilling water does not remove the chemicals from it, just kills the microbes.
1) Take as large a pot you can get with a lid. Get a second, smaller bowl or pot that can fit in it, and which can be heated.
2) Put the smaller pot inside the larger one, then fill the larger with enough water so that it does not over flow into the smaller one. You may have to go lower, depending on whether the smaller one tries to float. You might add a few weights, but make sure they are clean. The smaller pot is where your distilled water will collect.
3) Put the whole thing on a source of heat. Put the lid on the larger pot, but put it upside down, so that the handle (in the center) sits over the smaller bowl. This is what will collect the steam and then channel the drips.
4) Put something cool in the lid. This will cause a temperature difference and promote condensation. The article suggests ice, but I'm going to suggest you save the ice in a cooler. Add some water to it, then have several wash clothes, which you dip in the cold water. Put the wet cloth in the center of the lid. This will allow you to remove the cloth as it gets warm and replace it. If you don't have ice, a source of cooler water would probably work.
5) Turn the heat on. It doesn't have to boil, though high heat is better at killing microbes.
6) Keep an eye on the process. As the bad water boils, the volume in the larger pot will lower and the volume in the smaller pot will grow. You want to remove the now good distilled water at regular intervals. BE CAREFUL, you are dealing with very hot water capable of causing burns. Same with the steam from inside the pot. When you lift the lid, do so with the opening away from you.
This is not the best method but can do in a pinch if you need specifically distilled water for CPACs or other medical equipment or first aid. Most of us can probably get away with just drinking filtered water.
If you need for distilled water was more long term, I could see making a solar powered distiller instead, which used a copper coil condenser instead of ice.