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how does soap help to separate dirt from clothes?

Soaps are alkali metals of higher fatty acids .The most common form of soap is sodium stearate .(C₁₇H₃₅COONa ) .Soap molecule has a hydrophilic carboxylic acid (-COO)end group and a hydrophobic hydrocarbon chain. Clothes become dirty due to the deposition of dirt (dust or smoke along with oily /greasy substances ).Such oily or greasy dirt is not wetted by water. When a dirty fabric  or dirty cloth is dipped into a soap solution ,the hydrocarbon end of the soap anion dissolves in the oil or grease and the polar end (-COO-) is directed towards water .Thus a number of hydrocarbon chains get embedded into the dirt particle and a micelle is formed .This micelles are negatively charged .Being similarly charge they repel each other .These emulsified dirt particles (micelles ) get washed away in water during rinsing .