Americans are taught from a young age to be independent and self reliant. "Stand on your own two feet" is a common saying that means "Do it for yourself without relying on anyone else." Growing up with this as a strong cultural value, American workers often want the independence to make decisions regarding their assignments - especially how to fulfill them.
This shouldn't be equated with not desiring any direction at all. Most Americans expect their superiors to give them direction, but they want to be empowered with the ability to have a say in the assignment and the freedom to do it in their own way.
Therefore, in order to get the most out of your American employees, you will need to respect this fundamental value. If you try to control or manage every aspect of their job, you will be seen as a "micro-manager," a negative term meaning someone who insists on knowing or controlling every detail.
If, however, you want more frequent input from them, request regular update meetings, but resist taking control of what they are doing. If you feel the assignment is going in the wrong direction, clarify the direction and ask if they would like some assistance. If you want a certain process used, give them training on that process and explain why you want that process used. Americans don't have a very high opinion of answers like, "Because that is the way we do it" since it sounds like an excuse for lack of creativity, so you may want to think about this in advance.
These tips might be helpful to you in managing Americans around the aspect of independence:
Try to empower your subordinates with the ability to make decisions over their assignments and how they are done.
Give them a clear goal and support, but leave them alone to do it their own way.
Allow them freedom to work independently without being micro-managed.