I am an Attorney and represent many large companies throughout the US and Internationally.
This is a fairly simple process in the U.S.
If you don't have an address in the US, we will need a registered agent for you, but you will need to explain what services you are providing in the U.S. Depending on the services and what you want to protect, we can select the correct state for registration.
We will also need to verify that you are who you say you are, and making sure the documents reflect how your company is structured.
Since you're interested in an LLC, do you have other members or are there other unit holders (units are like shares for LLCs)?
I'd be happy to assist you with this process, it's a fairly quick process.