Add a simple notification to the downvoted post, visible only to the user that made the post, make it stand out from the generic looking close reason box, perhaps by using a white text on an orange background in a speach bubble arrangement with an arrow pointing at the downvote button for the post.
The notification would link to a new or existing help topic that lists common reasons for downvotes and explains things to do about it such as editing. Once the user has clicked the link or dismissed it, the link does not appear on that post again, even if the post receives additional downvotes after that time.
There is already an entry explaining what down votes are for
Help Center > Privileges > Vote Down
Use your downvotes whenever you encounter an egregiously sloppy, no-effort-expended post, or an answer that is clearly and perhaps dangerously incorrect.
There's isn't an obvious link between that and how to deal with a post that has been downvoted though. I'm not currently aware of any help topic that explains what to do with a downvoted post, it might help if there was one.
For new users specifically, in addition to adding the notification to the downvoted post, put an entry in their inbox, this will help to highlight the notification and make it easier for them to access it. Do this only for their first downvoted post, any additional downvoted posts will not cause a notification to appear in their inbox.