An easy and controlled way to do it is with a flash. The easy and controlled part is because you simply does a couple of exposures first to find the best setting of the flash. Then you can do the light drawing and each time you trigger the flash you get a perfectly exposed still frame.
HKJ is basically correct here, but in today's world it is easy to lose sight of what Gjon Mili accomplished back in 1949. It was no accident that LIFE Magazine referred to him as "a technical genius and lighting innovator extraordinaire". Back in those days photographers did not have electronic flash. Of course, they did not have digital cameras and many didn't even use light meters. In fact, in the early 1950's some photographers were still even using forms of flash powder or arc lamps to do "flash photography". Harold Edgerton invented the strobe light in 1931 but it remained in scientific laboratory use until many years later. Mili probably used magnesium flash bulbs which were expensive enough not to pop them off for test shots too often. In those days one didn't "do a couple of exposures first to find the best setting for the flash" because if nothing else, when on location you would have to develop the film to see what you were going to get even if he were willing to waste the flash bulbs. Even if he were not shooting in the dark, "syncronized" flash was not a common thing back in those days, so photographers had to time their shutter just right and use slow speeds.
Gjon Mili would have relied on his experience and knowledge to judge how to set his aperture and when to set off the flash. He would have had his camera on a tripod and allowed Picasso the spontaneity to do his "light drawing" in the dark and then set off one or more flashes when he thought it was the right time.
While today, what Mili did might seem interesting, amusing or trivial but in his day he was pushing the limits of what was being done with photography at the time and even today they are remarkable images. I am struck by the fact that Picasso's light drawings have a certain three dimensional quality, especially in the Minotaur drawing; one never seems to see this in other attempts at this technique.
P.S. Kudos to Flying Turtle for his impressive image! It makes me smile. And to HKJ also for his avatar!