In order to enable your writer profile, you just need to visit your profile page and turn on the corresponding toggle:
After doing so, just fill in all the information that will be displayed on your public page, namely:
Your blog/website URL
Your Twitter Handle
Then, just click the "Update my Page" button.
That's it. A "My Publications" section will appear on your account:
and you can always view your public page either at your profile or at your "My Publications" section: