As of now, we have no evidence that alien civilizations exist. However, we occupy and observe a very small part of a huge, perhaps infinitely large universe. I will tackle the question at hand supposing that we have found evidence of an alien civilization already, whether by telescope or satellite pictures, or other means of communicating information.
It would be a good idea to establish contact with a supposed alien civilization, upon finding hard evidence for its existence, for several reasons. There would be so much that we could learn from a species different from our own. I don’t personally believe that we will find alien life anytime soon, if at all, but the possibilities of exploring the cosmos and finding new species are exciting and exhilarating.
First, the main reason we would want to contact an alien civilization once we have evidence of its existence is to learn more about life as a whole. How do the aliens live, what their home planet is like, etc., and what their anatomy is like. These questions would help us learn more about their way of life, if they are willing to answer them for us.
However, there are dangers of trying to communicate with an unknown alien race. They could be hostile, or maybe even bent on conquering the galaxy. You never know what could happen when you’re dealing with someone or something you’ve never contacted or seen before. Regardless, the means of communicating with aliens from distant solar systems will not even be possible for a while due to our degree of current communications technology.
Another reason why it would be good to establish contact with an alien civilization is because they may be able to give us new technology that could benefit our society. For instance, maybe they have advanced communications and healthcare that could be very useful to us. If we try to contact aliens, though, we would have to be very careful and respectful of them, and be prepared to give them something in return for whatever knowledge they pass on to us.
While there are obvious risks associated with contacting an alien civilization if we find it, we should not be so cautious as to avoid it altogether. The probable benefits of knowledge and even technology that could be gained from such an encounter would outweigh the risk of hostilities and even open war.
