How fast are geostationary satellites moving?

From a Newtonian perspective, the equation for the speed of a satellite in circular orbit around the Earth at a radius r can be derived by equating centripetal acceleration to the acceleration due to gravity so that the speed v is the square root of the gravitational constant times the mass of Earth, divided by r. This v depends on the r, but the radius of an object in geostationary circular orbit around Earth can be determined by substituting 'two times pi, divided by the period' for the speed. Since the period of Earth's rotation, along with its mass are all known values, you can find the radius and plug that into your first equation to solve for the speed.