How does soap work as a cleaning agent?

A soap molecule is a long hydrocarbon chain with a hydrophilic (water loving) end and a hydrophobic (water fearing) end.

The hydrophobic end is lipophilic (oil loving). When the soap molecules come into contact with an oily dirt, the hydrophobic ends stick to the dirt while the hydrophilic end sticks to the water. Motion causes the water to move, pulling at the soap molecules, which pull at the dirt. As more and more soap molecules attach to the dirt it weakens its grasp on the surface.

Soon the oily dirt is pulled off of the surface. It is then quickly encircled by soap molecules until they form a shell around the dirt. This shell is called a micelle. Now we have an object whose exterior is water loving, meaning the soap has taken an object that was insoluble in the water and effectively made it soluble by producing an emulsion suspended in water.

The water is then rinsed away, taking the soapy dirt with it and leaving behind a clean surface.