Can’t figure it out. Shouldn’t this be automatic?
Tell us your operating system and you may get a specific answer - Tested on Linux and it was almost automatically on first start of zotero, which found my LibreOffice installation and the extension has been installed.
The default way: In Zotero, you can go to Tools > Extensions and enable LibreOffice integration. Restart Zotero and LibreOffice, and that should be it.
If the default way does not work:
It is possible to make a manual installation. This link describes how:
https://www.zotero.org/support/word_processor_plugin_manual_installation
The file to find is Zotero_OpenOffice_integration.oxt
If you open the file in LibreOffice (e.g. by double-clicking it) then “Zotero LibreOffice Integration” becomes part of the installed extensions, and the control panel for Zotero should be available. The installed extensions in LibreOffice can be checked in Tools > Extensions Manager.