My question involves court procedures for the state of: California
Our startup company is located in Thailand. We are currently facing an ex employee who is defaming us through libel and slander across various internet forums. We originally approached the local police on an extortion claim, as he demanded money or he would "destroy our company". That investigation is still ongoing with the police, however we have a much clearer cut case in the realm of defamation. He recently succeeded in getting one of our accounts on a social media network shut down because the administrator of that site did not want to deal with the problem, so they simply cancelled our account. This service is located in San Francisco, and we are interested in obtaining the correspondence which led them to their decision. They have refused to give it to us.
Libel and slander is actually a criminal proceeding in Thailand where we will be filing the case, however I understand that it is generally a civil case in the US.
My question is, what is the easiest and least expensive way to get a legally binding requirement for the social media network in question (located in California) to turn over the documents we need in order to prosecute our case (in Thailand)? We do not have a great deal of money to fight this case, but unfortunately we must do something to stop this misguided individual from continuing to make up stories about us. We have no idea what he might have told the social media company to convince them to shut down our account, but we must stop this before it gets out of hand.
Can anyone explain how the discovery process works within the US, and specifically the state of California, when the litigation is occurring overseas? I'm just trying to understand how to begin, and how difficult a challenge this is actually going to be.
Thank you for any recommendations or assistance.

