Disclaimer: I never actually configured or even used MediaWiki, but based on the docs you may want to consider the following.
From the Auth0 side there are a few authentication protocols supported (OpenID Connect, SAML and WS-Federation) so you would need to check with MediaWiki to see if any of those protocols be suitable.
From the link you mentioned I quickly found an extension that suggests support for OpenID Connect; after having installed this extension you should setup a client application in your Auth0 account to represent MediaWiki. I’m assuming this a normal web application so you should create it as regular web application client type.
Having created the client application you would then have the required information to configure the above MediaWiki extension, more specifically, you would have something similar to:
$wgOpenIDConnect_Config'https://[your_account].auth0.com/'] = array(
'clientID' => '[your_client_id]',
'clientsecret' => '[your_client_secret]'
);