This type of filter is a common solution to the problem of obtaining clean water in many parts of the world, especially rural parts of developing nations. It is a fairly simple process that involves only materials that are available in most parts of the world.
A friend of ours is away in Kenya working on various projects having to do with sustainability including filtering water for drinking. Where he is now, "water guard" tablets are used to kill bacteria, but it does nothing to improve the clarity or taste of the water so he has been experimenting with different filtering techniques. Unwanted clothes from all over the world are imported to Kenya so there is a wide variety of fabrics available which makes fabric a good option for filtration.
Note that this filter can only filter particles and color out of the water. It cannot filter bacteria or viruses. Water filtered through this filter is not meant for drinking, and should be boiled before being consumed.
This instructable is the culmination of a project for the Spring 2011 Stuff of History class at the Olin College of Engineering in Needham, MA.