You unexpectedly find another civ populating YOUR continent. After closer inspection of the tourists, you realize they don't intend to leave. In fact, they have claimed valuable tiles with their Civ color. In response you:
1) Welcome your new neighbor and invite it to trade with you and prosper. After all, at least you don't have to sail across half the world to find someone to talk to and we are all part of one big Civ color wheel family. They even offer to get you closer to Alpha Centauri by trading techs.
2) Guests are not welcome. Post signs all around their house that explains that trespassers will be shot. A lot.

In spite of complaints from the Health Department, post heads on spears to keep an eye on them. Just to be sure they get the point, draw the 'line of death' two tiles out to sea. Put a flyer in their front door that explains that a settler in a boat is a viable survival technique (remind them about the 'line of death' two tiles off the coast).
3) Immediately complain to the other Civs about the flagrant violations of your national sovereignty.

Extol the virtues of (YOUR) manifest destine and start a dogpile.
4) Watch the neighbor from your sniper scope on the second floor of the book depository.

Close the blinds whenever they look in your direction. When you are sure they are asleep, sneak over and work them over with a pipe wrench.
Ah, so many choices . . .