I am operating mac OS Monterey v 12.6.3 I downloaded the Libre Office application and placed it in my Applications folder. I have double-clicked on the application per the instructions but nothing happens. I had expected an icon instructing me to Install the program. What should I do?
Did I understand correctly that you downloaded the DMG file to your Applications folder?
The DMG file should be downloaded to your Desktop or your Downloads folder. Double-clicking on the DMG should mount it to your desktop and open the Installer window from where you would drag the LibreOffice application bundle to the Applications folder.
If you actually did do this, and not what I understood you did in my first sentence, then you may need to authorise first launch of the LibreOffice application. Usually you will be asked this by the macOS Gatekeeper. Alternatively, you might try right-mouse-button clicking on the LibreOffice application, and choosing Open from the context menu. Sometimes, you have to do this more than once for LibreOffice to start the very first time.
You also need to check that you downloaded the correct architecture version for your processor - aarch64 for M1, M2, M3, and x86_64 for Intel processors.