This is a page for a step-by-step tutorial on updating the MediaWiki, for future reference.
Step 1: Backup everything
ProleWiki already has a rudimentary and simple backup system, thanks to comrade MxAsh. We have the backup of the all files in another server.
Step 2: Download the tarball
Go to the webroot directory and download the tarball of the new MediaWiki release:
wget https://releases.wikimedia.org/mediawiki/1.39/mediawiki-1.39.0.tar.gz
And extract them:
tar -xvf mediawiki-1.39.0.tar.gz