When your user (with frontend user privileges) is logged in,
he will see 'New' under the news articles, and when it is clicked he is taken to the editor, but now it shows up only in frontend.
When you assign someone as Author, the article will not be published automatically.
The administrator must publish it.
To be able to publish the articles as well, this user must be a publisher
A small editor note and pencil beside the articles your user has made will be visible to him when he is logged in (in order to edit if needed)
ps. Remember next time to follow forum rules please, and start your own thread