In villages, people are still going with the traditional method to remove mud from the water and make it suitable for drinking. As far as I know, villagers use salt to settle out the clay and mud.
It's easy enough to purify clear water. There is another effective method, known as solar water disinfection method, or SODIS, calls for leaving a transparent plastic bottle of clear water out in the sun for six hours. That allows heat and ultraviolet radiation to wipe out most pathogens that cause diarrhea.
It's a different story if the water is murky, as it often is where people must fetch water from rivers, streams and boreholes. In the developing world, many people don't have access to clear water, and it's very hard to get rid of the suspended clay particles. But if you don't, SODIS doesn't work. The microorganisms hide under the clay and avoid the UV.
Thus, to purify your water, you first have to get the clay to settle out, a process called flocculation. One of the most abundant minerals on Earth does this job very well: sodium chloride, or simple table salt.
Salt is inexpensive and available almost everywhere. And it doesn't take very much to make muddy water clear again.
Salt works best when the suspended particles are a type of clay called bentonite. The technique doesn't work as well with other kinds of clay. However, by adding a little bentonite with the salt to water containing these different clays, most of the particles glom together and settle out, creating water clear enough for SODIS treatment.
You mean like in a survival situation?
Then maybe a lifestraw like this is handy: https://amzn.to/2WDXjWd