The most recent OLy version can always be found at the top of the Download page. (You can also look at the Releases page.)
The file you need to download has a name like OOoLilyPond-1.X.X.oxt.

In LibreOffice,

• open the extension manager (Tools -> Extension Manager),

• click the "Add" button which will open a file dialog,

• select the *.oxt file you've just downloaded,

• confirm with the "Open" button.

• When asked for whom you want to install the extension, you can choose "only for me" which won't require administrator privileges on your system.

• After successful installing, close the extension manager.

• Probably you will now be requested to restart LibreOffice.

After restarting, LibreOffice will have a new "OLy" toolbar in Writer, Calc, Impress and Draw. It contains an "OLy" button that launches the extension.
(The "Batch" button is discussed in a later chapter: Advanced features - Batch processing)

• By the way: Please make sure that you have LilyPond installed on your Computer. ;-)

Congratulations - you are now ready for the next chapter: Tutorial.
There you will find a last adjustment to do in the configuration dialog.

With some additional software from the net, you can further increase the possibilities that OLy offers you.
Here is a recommendation that you should not miss:

OLy's built-in text editor only has very limitied capabilities.
Working gets much more comfortable by using an external editor.

• Frescobaldi is a taylor-made editor for working with LilyPond files: https://frescobaldi.org/
  (Download: https://frescobaldi.org/download)