Suppose you looked up into the night sky and saw a star blinking on and off once a second, like a Christmas tree light. One star out of thousands; that would certainly get your attention. For ten thousand years people would think it was divine, and posit a god to explain it. Eventually they would realize it was a signal from an advanced civilization, and send a radio greeting. The blinking star simply says, "I'm here, come talk to me.", and radio transmissions do the rest. We know how to send and receive point-to-point radio messages across the galaxy, but how do you make a star blink?
Surround our sun in a shell of shades that can open or close. To simplify the geometry, place the shell directly on the sun's surface. Obviously these shutters are made of a very special material that we can't imagine today. The shutters open and close once a second, causing the sun to blink, but it isn't that simple. The trick is coordinating the action of all the shutters so that they open and close at the same time. It's not just an engineering problem, the concept of "simultaneous" is not well defined across large distances, as Einstein explained.
Place Amy and Bob in space ships one light hour apart. They both have lights that they want to turn on at the same time. Their actions are simultaneous if Charlie, floating halfway between the two space ships, sees both lights go on at the same time. In this case, Amy turns her light on and then sees Bob's light come on an hour later, and Bob turns his light on and then sees Amy's light come on an hour later. Temporal concepts such as before, after, and simultaneous depend on your reference frame.
Return to the shell of shutters around our sun, forming a sphere of radius 700,000 kilometers. At the start of this thought experiment, all the shutters are closed, hence no one can see our sun. At the sun's signal, emanating from the center, they all open at once, and remain open, turning the sun on so to speak. From the sun's point of view they all open at the same time, releasing a burst of light, but what does an observer see from far away?
Draw a line from a distant star to our sun, passing through the shell at a point c. Establish a plane p at the point c, tangent to the shell. Project sunlight onto this plane, traveling from the surface of the sun perpendicular through p and on to a distant star. That is what an astronomer sees from far away. The shutters at and around c open first, projecting a small circle of light onto p. Further out, the light passes through the shell, but then travels a small, additional distance to reach the plane p. From the plane's point of view, those shutters open a little bit later. The disk of light expands. Further around the sun, light has further to travel to reach p. 90 degrees around, at the edge of the solar disk, light travels 700,000 km to the plane p in 2.4 seconds. Within p, light begins at the point c and expands into a disk of radius 700,000 km in 2.4 seconds. But you can't see the expanding disk from far away; the sun simply becomes brighter until it reaches its full luster in 2.4 seconds. This leads to the time-change theorem in astronomy. If an object changes brightness or physical appearance in time t, it can be no larger than 2t times the speed of light. The change cannot be coordinated faster than that. People imagine a supernova exploding at once, like a bomb, but in fact it takes several seconds, or even a couple minutes. The explosion begins at one point and spreads throughout the star, which is several light seconds across.
Continuing our thought experiment, let the shutters open and close once a second. The disk of light within p is expanding around c, when suddenly it goes dark at c as the shutters close once again. The disk of darkness expands, pushing the ring of light outward, until another disk of light appears at c. Rings of light propagate outward as the shutters open and close, open and close. From far away the details of these rings are not visible. The sun simply shines with half its light and does not blink.
The easy solution is to open and close the shutters once a minute. A couple of seconds are needed to ramp up and ramp down, but that's not a problem. Throughout the galaxy our sun blinks once a minute, a clear signal that we are here.
As for our shutters, there is no material that can exist on the surface of the sun, nor do we want our daylight to turn on and off here on earth. Place the shell 300 million km from the sun, between the orbits of Mars and Jupiter. Now you can use ordinary materials, but you need a lot of them. The shell grows as r2.
Since energy cannot be destroyed, what happens to the sunlight that is blocked when the shutters are closed? It heats up the shutters, which then radiate energy in the infrared. Our sun now blinks between visible light and infrared heat. Indeed, Freeman Dyson suggested building a sphere around a star to harvest all its energy, whereupon such a star, enclosed in its sphere, would release all its energy in the form of heat. People have looked for these infrared signals, indicating a Dyson sphere built by a supremely advanced civilization, but so far none have been found.
Such a shell would be difficult to construct for any civilization, no matter how advanced. A ring is much easier, since it can be held taut by centrifugal force as it spins around the star slightly faster than orbital mechanics would suggest for its radius. But you can't do that with a sphere. The equator might form a nice tight ring, but the poles are not moving at all, and would droop towards the star under the influence of its gravity. No material that we can imagine would hold up under those forces.
Perhaps a ring would suffice however, if you just wanted our sun to blink in the galactic plane. That would signal most of the stars and most of the civilizations in the Milky Way. Since the curvature of the shell, or ring, is much less at this larger radius, it almost coincides with the plane p, at least for a couple million kilometers. When the shutters open, the light begins at the point c as before, but it expands to a solar disk in 3 milliseconds. We can return to our original blink rate of once per second.
Perhaps the ring could have a width of 10 or 100 times the diameter of the sun, to occult the majority of the galaxy, but at some point orbital mechanics gets in the way. The top and bottom edges of the ring are pulled towards the middle, trying to crunch the ring down to its equator, which is the true orbital plane.
Once again, people have imagined rings circling stars. A famous example is Ringworld, by Larry Niven. In this science fiction story, an entire planet is reshaped into a ring, to provide more area and more solar energy for its inhabitants. This is a Hugo award winner, and an absolute must-read.
Building megastructures in space will probably be beyond our technology forever, and there are surely better ways to harvest sunlight, or send omnidirectional signals throughout the galaxy. This is just a fun exercise.