If the Drake Equation is correct, then there are roughly 10,000 planets or other celestial bodies that have intelligent life on them at any given time in our galaxy, the Milky Way. So roughly, for every 1,000 light years, we should find one of these planets or moons containing intelligent life. The light (or images) from the closest of these celestial bodies would take 1,000 years (due to the speed of light) to get here even if we are viewing via telescope. So if we could observe spaceships leaving a planet's atmosphere, that would mean that this is what happened ... oh ... maybe 1,0000 years ago. The possibility also exists that we could be looking at a planet with intelligent life, that currently is in their space age, but we are looking into their bronze age because the image takes so long to get here. Mind-boggling once you start thinking about it.
It goes the other way as well. If an aliens species were watching us at this very minute, they could be watching the signing of the Magna Carta or the rise of the Pueblo civilization. They would not see our current highly advanced societies with our satellites circling the Earth not until the light we are transmitting reaches their telescopes some 1,000 or so years from now.
With this being said, one would think that the chances of a highly advanced technical people contacting each other, with two way communication, is not very likely. A very large window (time span) would have to be open when their respective civilizations overlapped. A world like that one portrayed in Star Trek, which is very pleasing and dreamy, is just not going to happen. We will never travel a short amount of time to meet alien cultures. I love that idea, it is a great plot device. But make no mistakes, Star Trek is good television, not good science.