Can you give me a simplified (but not too simple) example of how U.S. corporations control U.S. government?

US corporations do not control the US government. They may influence the government through political donations, lobbies, and other means, but that does not constitute control. The US government consists of three branches, and while some powerful corporate interests may be able to control a small segment of a branch, such as one congressman or an agency, there are too many checks and balances built into the system to permit control of the entire government by corporations.