Change "Activity or Calendar Events Info" in Garmin mobile Connect app watch face settings to "Google Calendar".
– If you don't see such option there, you watch does not support it.
Get a link and code from your watch
Enter the code from your watch on the given link (probably google.com/device)
When succeeded, wait for the watch to log-in. It can take 5 minutes or so.
The watch will load your primary Google calendar. You can change which calendars are shown in the watch settings.
– If you enabled a weather forecast as well, you'll need to subscribe for it before the calendars are shown.