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The easiest method of filtering water is to buy a quality water filter. Most families, staying put during a disaster (bugging in), will be well served by a Katadyn or Berkey water filters.
I can recommend the Katadyn Drip Ceradyn water filter or the Big Berkey water filter. Both of these filters are difficult to transport because they are designed for home or camp use. The complete filters are also expensive; you can reduce the cost of a complete filter by just buying the filter elements and constructing a filter out of five-gallon plastic buckets.
Now sooner or later, usually later with a Katadyn's Ceradyn and Berkey's black berkey filter elements, you and your family are going to have to construct a water filter out of available material. I have included two links to a "slow sand filter."
A slow sand filter uses sand, soil, and rocks in a 55-gallon drum to filter water. Make sure you read and print the slow sand filter plans from Surfer Without Borders. The other links should be read, printed, and placed in your survival bible as you see fit.
Surfers Without Borders - Slow Sand Filter Plans
How To Pedia - How to Filter Water with a Sand Filter
World Health Organization - Slow Sand Filtration
World Health Organization - Slow Sand Filtration in PDF format