Water purification
 

This has probably been discussed before, but how primitive can you make a purification system for water

Depends on the volume you want and what need to remove. If you are killing amoebas/paramecium that is one thing, if you are removing PCBs or heavy metals that is another.

The most primitive I know of requires only a sheet of plastic, a collection vessel, a hole, 4 stakes, and a rock.

I think most water will be simply filtered for large particulates (maybe through sand in a cloth) and then probably boiled if fuel is available.

Charcoal makes a great filter. I guess you'd start off by filtering out obvious sludge and particulates in your water, boil it, then use a finer filter (maybe with charcoal). That'd be a start right?

Edit: Hah! Kato posted his comment as I was writing mine!

Only two types of people in the T2k universe, the quick and the dead ;)

As I recall (it was some time ago) here in Australia we used to get issued a special cloth sack that was used to filter water. It wasn't exactly a rectangle as one side at the bottom was angled so water could drip into a collection container. I think it was called a Millbank Filter or something similar.
Anyway, the point was to fill the bottom with a layer of charcoal, above that a layer of sand and above that a layer of pebbles. Then you'd pour the suspect water into the top of the bag and let it filter through.
Obviously this was for survival situations as you couldn't carry the thing around while it was filtering