How does oil dispersion work?

I think you are asking how do chemical dispersants work on oil. There are a number of chemical dispersants available. As indicated in the related link, a dispersant must contain a solvent, which is a substance that can dissolve into the oil. It must also contain a "surface active agent" or surfactant. You can visualize a surfactant as a having two sides, one that "likes water" or hydrophilic and the other that "likes oil or oleophilic. In this aspect, it is similar to dish washing soap that "cuts through the grease."

However. the use of dispersants is controversial as chemical dispersant is not natural in the marine environment. It is a pollutant. To add a pollutant to an enormously polluting spill has caused controversy. However, the intent is to break up the spill, and reduce its impact as it comes closer to shore. Natural forces such as biological processes, evaporation and wave action further reduce or disperse the spill. Due to potentially toxic effects, no dispersant can be used on oil spills without government (EPA) approval. The government may put restrictions on what is used and how much is used.

Dispersants have been used for several decades. There are notable limitations particularly in heavy oil spills where the chemical will just run off of the spill. BP is injecting dispersants on oil as it comes out of the well- a new application. See related link.