There are many ways! We invaded Iraq and overthrew a government there (and have done so in other countries in the past, either openly or clandestinely). Trade influences other nations (as when we import cheap goods from low-wage countries, invest abroad, etc.). There are many, many ways.
Your text materials undoubtedly discuss this. Here are some other ideas:
http://www.bing.com/search?q=United+States+influence+abroad&FORM=EDGENA
How does the United States shape global affairs?
2 answers
Answer???!!???😒🥺