While there are many specific circumstances that can lead to a revolution (since that is essentially what overthrowing one’s economic and political structures means), there are two general rules that we can propose. We can say that revolutions tend to occur when people think that their everyday circumstances are excessively oppressive and when they think they have a real opportunity to mount a successful revolution. Both of these conditions must exist before a revolution can occur.
First, people have to feel that they are being oppressed to an excessive degree. People generally tend to stick with the “devil they know” for a long time. They do not try to rebel at the slightest provocation. But when conditions build up to the point that the people can no longer tolerate them, they rebel. We can see an example of this in the American Revolution. (Admittedly, many scholars do not see this as a true revolution.) The American colonists tolerated what they saw as excessive English taxation and regulation for a while without rebelling. However, when the taxes and regulations piled up, and when the British did particularly unpopular things like imposing the Coercive Acts on the colonies after the Boston Tea Party, the colonists were ready to rebel. They felt that their conditions were so oppressive that it was necessary to rebel.
Second, however, people need to feel that they have some chance at success in their rebellion. This is one reason why there were so few rebellions among the African American slaves in the antebellum South. They were terribly oppressed, but they knew they could not succeed in rebelling so they largely did not try. When something happens to give them hope, however, they will rebel. We can look at the Russian Revolution to see an example of this. When things went so badly for the Russians in WWI, the people perceived that the Tsar’s government was weak. They felt that there was a chance for rebellion to succeed. This was a major reason why the revolution happened in 1917 and not earlier.
Thus, we can generally say that people will try to overthrow their current circumstances when those circumstances are very oppressive and when there seems to be a chance to successfully rebel against them.
This is a very difficult question and I'm afraid that there isn't a single answer that's applicable for all groups and societies.
The most accurate answer would be that it varies. People have different reasons for revolting against a political or economic structure. But it is safe to say that people do not revolt, that is take up arms or violently protest, a system unless they feel that it is utterly unfair and that they are unable to live in such a system.
Different societies and groups actually have different tolerance levels for unjust systems or oppression. And different societies have different priorities. For example, when one group may revolt when their freedom of speech is taken away from them, another group may not see it important enough for a revolution, at least not initially. Economic inequality (wealth of a nation belonging to a small group of people), lack of opportunities (for education, jobs, health care, etc.) and political and religious oppression are main causes of revolts.
But how long it takes a society to revolt varies. Some countries have low tolerance for injustice and oppression and may mobilize and react quickly, whereas other societies may take a very long time (for example the Indian revolution against the British which occurred after hundreds of years).
Generally, if a society feels the need to overthrow the government it is for the reason that they feel they are being restricted. Whether it is a law that makes the people feel too controlled or if they feel rights are being taken, humans naturally want to rebel against those in power. There are many examples of societies overthrowing their government/those in power, but one that is most know is the American Revolution. The colonists wanted independence and not have to follow British laws (for things like taxes or boundaries), so we fought to become our own country.