It’s simple really. Just wait till the Sun lines up between the stones. It's great for calculating the summer solstice, but not really accurate enough for timing fast-moving Near-Earth Asteroids. Still, what a hoot for garden furniture! And you could have parties where everyone dances naked around it to welcome the coming of spring.
Jokes aside, I use Abouttime software over the Internet to set the time of the computer operating the CCD, and through that a time stamp is placed in the header of each FITS format image. I believe this gives accuracy of less than a second. Although that might not be sufficient for absolutely all tasks, it suffices for most of them. In addition, the scripting software, SBScripter, polls a time server to ensure that the computer time is accurate both before and after an image is taken.
One of the problems in determining the rotation period of an asteroid is that its period may exceed the hours of darkness available to any one observatory, so that an international collaborative effort is required. As dawn breaks at one observatory, another further around the globe still in darkness picks up the task in a kind of worldwide relay. Observations from different observatories are matched up to provide 24 hour coverage. The time clocks below show the time at some active observatories scattered around the world.
Getting back to Stonehenge, there are many theories about its use as an astronomical clock. One of the interesting theories is that by Duncan Steel outlined in his book, Rogue Asteroids and Doomsday Comets (Chapter 8). Steel conjectures that the original Stonehenge (Stonehenge I) was built to measure and predict meteoroid storms following some Tunguska-class impacts some 5,000 years ago.