Now let's review the same circular motion of the can of beer but in a rotating with the can system of reference. It is not mystical centrifugal force which slides stuff off the dashboard of your car every time you make a turn, it is your car which moves away from the straight inertial motion of the stuff, so for you this straight constant line motion appears to be different. Fortunately, Earth pull is strong enough to hold us and air, etc. on the surface. So, Earth is constantly falling toward Sun - instead going along a perfectly straight line it's velocity vector constantly rotates toward Sun making what we call orbital motion.
Black holes move around the same way any other mass does.
Two black holes orbit each other the same way any other two objects do. Because they move with high acceleration, they generate strong gravitational waves radiating their kinetic energy away. As a result, instead of following stable elliptical orbit, they spiral onto each other with increasing orbital velocity. UTC Quantum and classical models of gravity.