It's two detectors, each of which has two tunnels at right angles to each other (and generate an interference pattern when a gravity wave distorts the tunnels length).

Oops, I meant two.

I'm no expert, but wouldn't you need an extremely long baseline to triangulate on distant stars? I mean, too long to fit on planet earth?

Only if your interested in the distance, parallax measurements do that by measuring when the Earth in on different sides of the sun.

If you're only after direction you can measure the time skew between signal hitting detector one and two.As you know the speed (same as light), and that the wavefront is parallel, you have a pretty good idea where in the sky the wave came from.

For the first case, you would need a signal that lasts for at least half a year. Does that cover two black holes merging?

Well, technically, they black holes circle each other for billion of years. So with instruments sensitive enough, you could do that. Unfortunately, LIGO and the others are only sensitive enough to see the last few parts of a second, when the signal is strongest.