News articles can be approved from the Front End by users with Full Control Access.
When a news article is submitted by a user with appropriate access, that is, Read Only and higher levels, an email notification is sent out to the full control users informing them that they have an article to approve.
The email body contains a direct link to the submitted article (as shown below) clicking onto which users are taken to the page with the news article in the editing mode, from where they could either edit the article, approve the article, or they could delete it.
Also available from within the My Content area in the Top Toolbar, clicking on News here will take Full Control users to the My News page where you can view the list of all the articles awaiting approval.
From the list you can select the desired article, and be presented with two options Edit and Delete at the top of the article.
Clicking on Delete will remove the news article, that is, delete it before it goes live. Note: once it is deleted there is no way to recover the article
Clicking on Edit button gives the users the option to view the news article, also to further approve / delete the same or send it back to the submitter to make changes.
Select the desired option from the drop-down menu, and then click on Save and Submit.
Once approved the news article will get displayed within the News category in the Front End, and the submitter will get a confirmation email.
Note: By selecting the article from the Requires Approval area you'll need to select edit or delete first before progressing. You do not get these options from the email link.