Can someone explain me how the FBI works?

Hello, everyone.

I'm writing from Italy, so, I'm sorry for any mistakes that I might make.

I've recently heard about the FBI shutting down websites such as "Megaupload", for alleged copyright infingment. I've also read that the website actually had its legal quarters in Hong Kong or such.

So, my question is, can the FBI shut down a website that is not legally located in the US and make it unavailable all over the world? I mean, there are probably countries in the world where the copyright laws are different, so wouldn't it be a "crime" towards these countries to shut down the website worldwide? Why not take it down just in the US, or remove all copyright-infringing content?

I mean, which are the laws that allow the FBI to take an action that has recupercussions even outiside the US?

I don't want to discuss about file sharing and how legit it is, I'm quoting Megaupload as an example just because it's the latest one, but this thing about the Federals has been nagging me for a long time.

So, I'd like to understand how far the powers of FBI can reach, what are its competences in and outside the US (for example, a murder is dealt by local police or FBI?), since I'm a foreigner with little to no knowledge about US laws and US military corps.

(Also, military forces in Italy are really, really different!)

I'd also like to read more about it, do you have any good references apart from Wikipedia?

(Again, I'm sorry for my English!)