Buy a domain. Setup a web hosting account […]. Install WordPress or hand-code a website for this account. Let people follow you directly by checking your site, or subscribing to an RSS feed or email newsletter.
It was like that couple of years ago, then social media made really really easy for everyone to tell their story. The problem is that your story is now tied to some company that controls basically everything outside a textarea which you use to tell your story. That's way more limiting than having your own website or blog which you control as a whole. Sure, it takes a bit more work to set up a website and you may have to hire a professional to help you, but it's way more satisfying at the end than creating a Twitter account or a Facebook page.
One more thought for Twitter users: if you want to tell something which needs a thread of multiple tweets then write a blog post instead. That's how we used to do it.