Rock boiling: heat rocks in a fire, then place them in your water container (with water) and boil the water.

Construct a filter from a cone of birch bark, fill it with grasses and sand in layers. Unfortunately, this doesn't get rid of pollutants.

Construction of a solar still will help to naturally purify water. Just pour the contaminated water next to the solar still (not in it), and the filtered water will be drawn right out of the ground and collected in the cup in the still. The same can be done with human urine.