Installation 

This version supports TYPO3 12.4 LTS and 13.4 LTS with PHP 8.1 to 8.5 (as supported by the respective TYPO3 version). For TYPO3 11.5 LTS use version 12.x of the extension.

Composer 

composer require svent/pageclasses
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Then update the database schema, e.g. in Admin Tools > Maintenance > Analyze Database Structure.

Without Composer 

Install the extension pageclasses from the TYPO3 Extension Repository (TER) in Admin Tools > Extensions. The database fields are created during the installation.

Include the TypoScript 

Add the static template Pagewide CSS Classes (pageclasses) to the main TypoScript template of your site: Web > Template (TYPO3 12) or Site Management > TypoScript (TYPO3 13), edit the whole TypoScript record and add it in the field Include static (from extensions).

That's all: the TypoScript of the extension sets page.bodyTagCObject (see setBodyTagCObject), so the classes are rendered without further configuration.