Believe it or not, it was probably clocked with the same technique that a police radar gun uses...
Police radar guns work by bouncing microwaves (IIRC) off your car and then measuring how much the reflected wave's frequency has been shifted by due to its encounter with your moving car.
Astronomers can use the exact same principle to determine how fast stellar objects are moving towards/away from the Earth, except that they don't need to bounce anything off the star, since the star is conveniently emitting its own light which can be analyzed to determine how much its frequency has been shifted up/down from its "base" frequency due to the motion of the star as it emits the light.