what is the best way to expose the contradictions of people, and organizations, and institutions whose behavior eventually benefits few?

It all depends on the context of the specific situation. You can use the standard expectation and practice of ethics and address it if you run into unethical situations but as I said the execution will sometimes depend on context. There isn't a single light switch approach to solving it.

Ethics: moral principles that govern a person's behavior or the conducting of an activity

Morals: a lesson, especially one concerning what is right or prudent, that can be derived from a story, a piece of information, or an experience

Ethics and morals are as contrast between individuals as opinions and beliefs. Which, in essence, can be seen as one and the same. What is ethical to one is unethical to another. This could basically be boiled down to an argument of semantics. If you are referring to something that is unethical AND illegal...then there are a multitude of steps to report such violations.

If you are studying ethics, then try to live ethically. To what end are you trying to expose people and organizations? Do you have proof of wrongdoing? "I am studying ethics" means nothing. Explain yourself.