Well it depends on the circumstances of how the gate appears.
If it just pops up out of nowhere, with no explanation at all..
one: nations would go to defcon 2 really really quickly. Then after days, weeks, we'd calm down, then we would send up some probes, maybe manned to look at it.
Now the next thing is.. is this gate one way or 2 way? If it is one way, then we would end up sending probes through, and nothing comes back, not even radio, so we wouldn't know where it goes, so if its that way, then you'd have these loonies that would jump at the chance to get through. while most would be hesatant.
If it was 2 way, then a probe would go through, and come back, and tell us where it was. does it go to a new planet? Out in the middle of no where?