The ability to publish posts is only available to admins or registered users with adequate permissions. This means that non registered users cannot publish posts. Posts submitted by non registered users have to be moderated.
To publish a post, simply change the status to Published as shown below:
From the data view page, either
Individually or
Highlighted: 3 dotted icon in the post card.
Highlighted: Publish button to publish a post
in Bulk
"Mark as" drop down menu for marking a post in bulk as published, under review or archived
Highlighted: Published button under the "Mark as" drop down menu.
From the post detail view
Highlighted: 3 dotted icon in the post card.
While editing a post
Highlighted: Published button under the 3 dotted icon drop down menu. to mark the post as published.