I'm hooking it up to replace a momentary button that is currently in place in a device.
Still more information needed. The device could have a normally open or normally closed pushbutton ... its probably NO type. The device could have it's own pullup or pulldown resistor or none. The device's voltage could be 3.3V or 5V or other.
Most importantly, is the device compatible with a latched signal? Note that the button will not return to a default state - it needs to be pressed again to toggle.
Anyways, as an example to test the switch only, try the first set of contacts connected as a latching toggle switch. Connect terminal 3 to GND and terminal 2 to an Arduino input configured as INPUT_PULLUP. When the switch is in the down position, you should read 0 (LOW). Up is open - the input will be pulled HIGH.
If you use terminal 1 instead of 2, When the switch is in the up position, you should read 0 (LOW). Down is open - the input will be pulled HIGH.
Same idea for the second set of contacts. Another method is to use a pulldown resistor configuration.