The Report extension adds a special page for users to privately report revisions of pages for admin attention, as well as another special page for admins to handle such reports.
Report is on the MediaWiki extension distributor. Follow the instructions on the extension page to install it from there like any other extension.
From the root directory of your wiki, run the following commands:
cd extensions git clone "https://gerrit.wikimedia.org/r/mediawiki/extensions/Report"
Then add the following line to your LocalSettings.php:
wfLoadExtension( 'Report' );
Finally, from the root directory of your wiki, run the following command:
php maintenance/update.php
This will create the necessary tables that the extension needs.
Once it's installed, it's in use! The extension adds links next to every revision for reporting them, all of which lead to Special:Report.
For admins, simply navigate to Special:HandleReports to view reports that need handling.