agudauskas:
Which wire(s) are for Ground and which for connection to Arduino digital (?) PIN.
You could take the White to a digital pin and the Black to ground (or vice versa, doesn't matter), but make sure you use pinMode(pinnum, INPUT_PULLUP); so the pin's at 5V normally. Then when the relay flips the pin will go low- look for a low in your logic with a digitalRead();
Describe what it is you're trying to do: what's the Arduino role here, since it seems to me that usually that sensor controls say a driveway gate motor direct.