America's main export is the culture. Their entertainment industry is in high demand all over the world, and with consumption of movies, books, games, forums, people also become to revere American values and America itself. After that, it's easy to lean on other governments to enforce American laws, defend interests of American companies and protect American interests.
Whole world pays for the right to enjoy American entertainment and copy American bytes. It could be not a bad bargain, but result is, America thinks for the whole world, and this thinking benefits America first. USA sucks resources from entire world, leaving behind the good feelings and relaxation from not having to think independently.
How to end American cultural hegemony? The hard way would be promoting own language and culture, but in modern world it's very hard to pull such a stunt. Easier option is to become influental in american culture and change it from within.