Most network marketing companies come with a blogging platform, your sub-domain is also under an authority site which might help you get search engine traffic. So use that blogging platform and if your network company doesn't have one then you can create one yourself.
Create valuable blog posts (use images, text, video, infographics or even audio) use those blog posts to build trust with your social media audience. Each social network has it's own approach so I would advise you to do some research on individual social networks, I won't get into that.
You can go to youtube and start typing things like: "promote MLM on facebook"... "how to build an MLM business using twitter"... "google plus tips for network marketers" etc.
Social media marketing can take a while, so understand that it will take some time for you to build a responsive audience. So I would advise you to start with a facebook profile and group/community. Your target can be to add at least 5 to 10 people to your facebook group a day for instance.
Social media marketing works well with content, so also do some basic research on content marketing as well. This will help you to avoid getting overwhelmed with coming up with great content all the time (Writer's Block). There's no need to use original content all the time, you should learn how to take content that already exists and present it in a unique way. You can also visit old blogs and re-write their outdated posts and make it fresh.
Make sure that your content is worth sharing, when people share your content on social media and other online platforms, they make your marketing job a lot easier. Also make it easy for your audience to share your content by having sharing buttons on your blog/site.
That's how I would promote a network marketing company via social media, by simply using a blog. But don't rely on one traffic source, also check out things such as guest blogging, SEO, video marketing, email marketing (which most likely is part of the mlm program), forum marketing etc. always diversify.