Show user's articles on Profile tab

I'm sure this is a stupid question, but how would I go about adding a tab to a User's Profile that allows them to A) see any articles they may have submitted and allow them to edit their article, if necessary?

Thank you for any suggestions in advance.

see any articles they may have submitted

Articles tab from CB Articles already provides that.

allow them to edit their article, if necessary?

CB Articles and its Articles tab has no create/edit functionality, but they could use it to find an article and navigate to it then use the edit button provided by Joomla when viewing an article. Your alternative is to use CB Blogs.

Yes, thanks for that. I'd forgotten to allow them permission to edit their own articles! Bangs head against wall.
Got that figured out, but unfortunately once they edit their own article, they are currently allowed to edit anyone's article which is strange.

They shouldn't be able to edit other users articles if they're just given the Author usergroup. That usergroup by default only has permission to create articles and edit their own articles. If that's not the case check your permissions within Content > Articles > Options > Permissions. Your alternative is to use CB Blogs which doesn't require any additional permissions and can use Joomla, K2, or its own internal database for blog storage.