This is a great question. It is probably best to start off by saying that there is not only one way in which people of a lower social class challenged people from a higher social class. Each society will be different in how this is done. In light of this, let me give you some examples from history.
First, perhaps the most obvious way is through some sort of revolution. For example, in Roman times, the lower classes refused to go to war to combat a foreign army. When this happened, the upper classes had to compromise, or risk destruction.
Second, at times, such as with Martin Luther King Jr., people demonstrated in a peaceful way to show the injustices of society. In other words, by peaceful demonstrations they were able to show the intolerance and evils of society. I would say that Gandhi and Nelson Mandela took this approach as well.
Third, at other times it was more violent, such as the French Revolution. Keep in mind King Louis XVI was executed.
In the end, the most important points are the following. First, the lower classes acted together. There has to be unity. Second, they created their own ideology and have a goal in mind.