Step 1: Turn on what uses it
In the admin menu: Setup & help, then Settings, then Features
Google Calendar appears once "Rentals" is switched on. Google Calendar for private lessons is coming soon.
Step 2: Connect your Google account
In the admin menu: Setup & help, then Settings, then Integrations
Click "Connect Google Calendar", sign in to Google and allow every permission it asks for. You come back here and the status reads "Connected". If you untick a permission, it is not connected; try again.
Step 3: Choose a calendar for each room and instructor
In the admin menu: Setup & help, then Settings, then Integrations
Under "Room calendars", pick the Google calendar each rental room's bookings go on. Under "Instructor calendars", pick each instructor's calendar: anything busy on it keeps private lessons from being booked at that time.
Step 4: Disconnecting
In the admin menu: Setup & help, then Settings, then Integrations
"Disconnect Google Calendar" takes effect at once, with no confirmation, and forgets every room and instructor calendar you picked. After reconnecting you pick them all again.