Let's say that by analyzing the light being emitted by distant stars that we identified an anomaly. The anomaly whilst not proving that alien life exists, does match the kind of characteristics of the light might look like if a race of aliens had successfully built megastructures in their solar system.
Well, we don't have to imagine this scenario too hard because that is exactly the scenario we are looking at right now.
I'm sceptical but open minded about it, and given the distances involved (some 1500 light years from Earth) we may never get to meet them (if exist).
But one part of me wonders how we might initiate contact, start to communicate and eventually meet face to face. Initial contact would be by radio communication obviously.
Each transmission would take 1500 years to reach across that distance. Because you would have no guarantee that they are looking our direction you'd have to continually transmit a signal over a long period of time to increase the chances that they detect the transmission. The analogue signal would have to be obvious to stand out from the natural background radiation and have hints in it to allow for the more sophisticated message to be contained within.
Perhaps this is the genius behind the film Contact which is one of my favourite movies. Unlike the film however, without some amazing leaps forward in our understanding of the universe we wouldn't be teleporting anyone anywhere too soon (if that is even possible).
Instead we'd have to embed enough mathematical and scientific principals in the signal to allow them to understand how to decode more deeply embedded data that we might send to them. We'd then want to encourage them to start sending a signal back to us. So we are probably looking at best - a 3000 year turn around time until we even got confirmation that the aliens existed.
Assuming that they did get our signal and responded we'd want to simply start exchanging historical and cultural information continuously as well as perhaps sharing our plans on how we might be able to meet some day.
Getting a living human being to KIC 8462852 would take a generation ship (that is, a ship in which many generations lived and died). At the moment we don't have the technology to sustain life in space like that, although it is actively been worked on since we are talking about manned missions to Mars. Assuming we did eventually come up with a way of doing it how long would it take?
Currently the Voyager 2 space probe is travelling at about 15km/s. Light travels at about 300,000km/s and KIC 846852 is 1500 light years away - so it'll take a while. And you can't simply divide the distance by the max speed of your fastest space ship because you need to have a relatively gentle acceleration curve not to turn the crew members into pulp.
Thats assuming that you can pack enough fuel to get the kind of ship required up to speed in the first place. Assuming we could get to our nearest neighbor star, perhaps we could come up with a way of using it to slingshot our way progressively across the universe. More efficient fuel wise, but dramatically longer journey as well.
I guess the good news it that by the time we managed to meet our new friends we would have had a long time to get to know each other and so perhaps the initial meeting whilst momentous might be like meeting someone that you've been chatting to online for a long time (applied at a species level).
Whilst I think it is unlikely that we've found another civilisation amongst the stars, I do believe that life does exist out there somewhere - it is just in the enormity of space we might never come across it. Then again, look at the hypothesised discovery of flowing water on Mars - a precursor to life (as we know it), perhaps finding another sentient life form isn't impossible.