I try to describe another boyscouts diary entry: water purification with nothing than a stone knife and a rag.
To craft a charcoal absorber some things need to be implemented first.
We need charcoal fragments remaining from burned fireplace as a resource and the possibility to collect sand from a river bed or any other proper place.
Additionally we need to cook water and refill it to a bottle, but this has been mentioned earlier.

Crafting a filter starts with cutting of some bark from a tree. Usually you would prefer some sort of soft bark like birch, because this bark can be bent without breaking.
The bark in hands we form a funnel and layer the filter material in it. The rag at the bottom covered with sand, crumbled charcoal fragments and some small stones on the top build the layers of the filter.

Water filtered by a charcoal absorber is almost free of organic remains, concentrated chemicals such as trihalomethane and microscopically small contaminants like herbicides and pesticide pollution. The last step is cooking to clean the water from any remaining pathogens.