Login to Medium and click on your user avatar on top right, then click "New Story". For editing a draft, click on "Stories".
Also can click on "Write a story" in larger web view.
Write your post. Save as a draft if it's not finished.
Once you're ready click on the green Publish menu. You can always edit later if you need to.
Once the post is published you can add to a publication.
Use the menu at the bottom of post, click on three dots, and then "Add to publication".
Choose the MEA 300 blog and click Submit.
I will get a notification to review and publish your post.