You can either go directly to your story editor by 1) going to your My Drafts and Stories/Manage Stories page OR 2) modifying your story URL and changing it to "edit" in order to access the story if you are already logged into the website.
1) When you are in your My Drafts and Stories/Manage Stories page, you’ll see the “Edit” button under each story, and that allows you to access the story editor and make changes.
https://www.inkitt.com/stories/000000 - STORY LINK
https://www.inkitt.com/edit/000000 - EDIT LINK
When you are in your story editor, make sure to click "Save" on the left side so changes are saved too.