Method of purifying salt water, but it works well for any kind of water, even heavily soiled water, nearly mud.
Pour the water in a pot with a matching lid (5 quart is good but 1 quart will suffice), bring to a boil, turn down the flame so as to have a very low rolling boil.
Add a heavy drinking glass with a thick bottom (rock glass) like you find in bars, so it doesn't float.
Place the glass in the center of the pan and put the lid on the pot upside down, the steam collects on the lid and runs to the center and drips off the handle/nob and into the glass.

If the water is suspect, boil it for nearly thirty minutes to kill all bacteria and parasites, and don't boil on high, in that some water may splash into the glass.
Remember, all you want is slow steam to collect in the glass as condensation.

Let cool and you have fresh water, but remember, its only water, so if you plan on living off this method for any extended period of time, you may want to consider a multi vitamin/mineral tab since the water will be void of all minerals.

The same technique can be done using a plastic sheet over a hole on the ground.

You place a container in the center of the hole, lay the plastic sheeting over the hole and weight it down around the perimeter. Place a smaller stone over the center of the sheet to form an inverted cone.

Now, dig a shallow trench around the perimeter of the sheet. You can place plant matter in the hole, pour contaminated water in the trench or even urinate in it. It will soak through the ground and evaporate. The water droplets form on the plastic sheeting and flow towards the center, dripping into the container.

You can add a long tube to drink directly from the container, but it's preferable to remove the container and add a couple drops of chlorine bleach.