In the era immediately following the coup that overthrew jacobo árbenz in 1954, how did the united states maintain its influence in guatemala?

I don't know what your History teachers will teach, because this still a pretty classified time and area right now. But most of our influence was through the CIA an their clandestine service (basically spies) that would pay off the government, help control and train troops, and use propaganda against the people.
Once again though, I don't know what your teachers will teach, so you should see works or not. 
If so, I am glad I could help,
If not, I am sorry, and I hope you can find what you are looking for.