If the people have motivation and cooperation then an easy solution would be a march on the capital. Something similar to the MLKJ march on Washington. If the government is corrupt, it is likely they would use the army to prevent this from happening, even going so far as to kill citizens. Harmless protests such as the Hong Kong protests, where the Chinese government gassed its own citizens.
In situations like this, if the population really believed in its dream, they would over power the government in sheer numbers. Generally, the army is not big enough to fight off thousands of people pushing their way -- without fear of death -- to the capital to fight the oligarchy. Generally speaking, a government would not want to slaughter its citizens, no matter how corrupt. Being in places of power over people is only useful if those people are around, so if they are dead it will be hard to have the power. In addition, there are many political problems with mass slaughtering citizens; if there were another country like America in your world, it would most likely go to war with this man-slaughtering government. I digress, if the people have a spokesman who can rally them, it is usually game over for the government.
If some politicians aren't corrupt then those politicians could influence governmental decisions by voting for or against certain actions. This is assuming it is a democracy, or some form of dictatorship in which more than one person is in charge. If it is only one person, politicians could over throw the president/chancellor/general by disobeying orders, whatever that entails. Not passing on information, causing the Commander and Chief to fall into a trap, perhaps.
If a company has money then the company could buy out the politicians. Assuming they are corrupt, more money would be welcome. If the tech giant did not completely control the government (directly make decisions, such as "I pledge allegiance to the United States of Walmart"), then they would be able to manipulate the politicians to cast votes, or to not pass on information to their Commander and Chief, etc. If you're thinking the government would shut the business down, you're wrong. The business would be sensible enough to hire its own mercenaries and fight its way to the capital if need be, or at least defend its operations, factories/plants, and HQ.
If there are immigrants then the new population could influence the votes in just a generation or two. This may seem racist, but flooding a country with new citizens has a huge impact. Once those citizens' children are of voting age, they could easily be 20% of the voting group, which is a big deal in politics. Such groups could even make their way into political offices, and get voted up the chain of command. In this case it would be best for each family to have four or five children to adequately increase the votes.
If necessities are held hostage, such as water sources, food sources, and power sources, then those can be used as bargaining chips. If these are controlled by a company, a mass of citizens, or armed troops opposed to the government they can threaten the government by limiting access. Taking out Hoover Dam or a nuclear reactor would certainly slow things down and get attention.
Most of these situations assume that the population of each group act as one entity, like an ant colony. This is dire for the operations to work. One person in the group with information could leave the cause and foil all the plans, even get people killed. There needs to be trust, motivation, and leadership in any of these overthrowing parties.