Happy to help! I’ll start with other places you can post your work. The names I hear the most are Newsbreak, Vocal, and Quora. They all have their own niche. Newsbreak is about news stuff mostly. Vocal seems to be mostly for creatives, though don’t quote me on that; I literally just signed up there yesterday. And Quora is for posing and answering questions. If you can get accepted to Newsbreak, they have a pretty great deal for new writers.
On Medium, promotion starts with your tags. You’re going to want to make sure you pick the best combination and take advantage by choosing the full available number of 5. Then, the most important things are curation and publication. Every piece posted is examined by the Medium curators, and they can choose to select it for “Further Distribution.” This means it’ll show up in people’s feeds and stuff. You’ll immediately see your readership increase drastically if it’s selected for distribution; there are some guidelines for what will and won’t be curated. Anything too promotional, not of much broad interest or dark, about Medium itself, or just low quality is sure not to be selected. And you’re going to need to have your post “metered” — that is, behind the Medium pay wall, meaning people have to pay the monthly membership to read it. You have an option for this whenever you go to post something, and it’s the only way you get paid.
The publications on Medium all have their own following, so by submitting to them, you can increase your readership through their followers. You can usually find submission guidelines on the publications’ pages. The publications all have different themes. You can find lists and descriptions of them online.
Medium is also very community based, so one of the main routes of increasing the attention your work gets is by doing what we’re doing right now: interacting with other writers and their work. If you go through and read, highlight, clap for, and comment on other people’s work, most of them will come back and read your stuff.
I, personally, am trying to build a social media feedback loop, so basically just spamming the zone by creating an Instagram, Twitter, Facebook, etc., and then promoting the same work, in different forms, on all of them, along with the other platforms, so that followers migrate from a wide web back to my Medium and vice-versa. (Well, and hopefully buy my book, which is really a main focus, but a story for another day.)
Lastly, there’s something called SEO (Search Engine Optimization). I don’t know much about it, but I know you can edit it on your articles, and I believe initially it reflects the “subtitle” of your article. The goal here is basically to match the words people are searching for on Google so that your Medium posts automatically come up there.
That’s everything I can think of at the moment; I hope I didn’t miss anything. You’re going to want to read an article or two on all those areas I’ve listed, as I don’t know enough to go into detail on them. Information on each is, however, readily available. I’d also recommend reading an article on going viral; there’s usually some interesting takeaways. And I’d look at other people’s writing for formatting ideas; the look of digital media is more important than you might think. Also, remember to always add an attribution to any stock photo you use.
Hope this helps! All the best!