Booking calls it "Calendar sync". As with Airbnb, the operation is done twice.
Bringing Booking's calendar in
Extranet → Rates and availability → Calendar sync → Export calendar. Copy the .ics
address and paste it into your dashboard under Calendar → Add an external calendar.
Sending your bookings to Booking
Copy your own export link and paste it into Calendar sync → Import calendar.
The room trap
Booking works per room type, not per property. If your listing has several types, there is one link per type and they must be handled separately. Pasting one type's link into another's calendar creates blocks that are very hard to diagnose later, so check the name inside the link before you paste it.
Delays
Booking refreshes its imports on its own schedule. As with every iCal sync, a double booking stays theoretically possible on a much-wanted date: on those periods, block by hand rather than relying on the sync alone.