Your stories can be reordered by simply dragging and dropping them around your Exposure site. Just drag the move icon, and then drop the story where you want.

Hover over a story to see the Move icon in the top right of any published story. 

If you don't reorder your stories they will be listed newest to oldest. Newly published stories will appear first unless moved around.

New drafts will be listed at the top of your stories unless you have more than 6. If you have more than that, a "View Drafts" button will appear on your screen. With it you can simply toggle between your Draft and Published stories.