What’s the process that makes it good at something so far off from its composition?
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To put it simply, things that are oily will dissolve in oily substance (meaning they are non-polar). The other stuff tends to dissolved in water, like salt for example (this is a polar solvent. What soap does is take an oily like molecule, attach to that a part that dissolves in water and you have soap. When washing clothes for example, say with an oily stain, the oily part of the soap molecule will help dissolve, or clean, the stain. But the washer uses water right? That is polar, so you need to get the oily material off the clothes into the water somehow and wash it away. Well the oily part of the soap has already dissolved the oily stain, now those soap molecules will form a “liquid” soap bubble around the oily substance. Remember one side of the soap molecule is oily, they will all point in towards the dissolved oil, with the other side pointing out, so you end up with tiny spheres of soap molecules surrounding the oily stain material. Inside that sphere is the oily tails of the soap and dissolved oily stain, on the surface of that sphere are the part of the soap molecule that dissolves in water. Now you have these tiny spheres that can be suspended in water because that little sphere on the surface has polar water dissolving part of the soap, inside has the oily tails of the soap in a little sphere that can float around in the water. Wash all that water away with all these little spheres in them washes away the oily stain along with the soap that surrounds it, now you have clean clothes. This same general principle works when using soap on other things while washing with water too.
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