For messaging, learning how to write a good business type letter is a good idea. First off, research your question before asking, as many times they have your answer in a FAQ or something, or even you could easily figure it out on your own.
Make a quick intro about something you appreciate of theirs and then a quick respectful request for what you want from them. Remember that they don't want to spend a lot of time reading emails. Remember that you still may not get a response.
Here's an article that seems to cover it decently:
http://www.artofmanliness.com/2012/03/01/how-to-write-an-email-that-will-actually-get-a-response/Realize that you probably won't create any sort of relationship from a short business letter. This is more for when you just need certain information.
As for networking, it can be pretty simple. This is for face-to-face world, but you can modify it for internet ( Remember that internet can be harder to make solid relationships).
You have obviously already connected with your current producer friends. Take one of them out for lunch or whatever and talk to them about what they do and whatnot, and request that you can meet up with their producer friends. Your circle will begin to grow as you meet more people and their circles, and eventually you may just find yourself eating lunch with somebody with important pants on.
In the real world this is a great way to get to know a lot about certain kinds of work, and also develop friendships with people that can offer you good opportunities and knowledge. Assuming you are competent, they are much more likely to hire you if you are their friend then if you are a nobody in a large crowd trying to get the same position.
On the internet, you may be able to do this through Skype or other social media. When talking with one of your friends, make an excuse like a three way collab, project, or something (or even playing a videogame multiplayer) to get one of their friends added into your circle. Remember to be real; being that dude that never says anything again bouncing around everywhere trying to take advantage of people isn't the reputation you want.
Simply rinse and repeat as desired.
Think of it like this: would you more readily accept a request from a random dude from nowhere, or somebody that one of your best friends is introducing to you?
Good luck getting attention of somebody you have absolutely no connection with, because you'll need a lot of it.