How to serial connect arduino galileo to alarm system
First of all, you'll need to make sure this is UART and not another protocol. Don't worry, if it's not UART the worst thing that could happen is jumbled data.

After that, you will need a 12v to 5v (or 3.3v) logic level shifter. When you have that you'll need to connect the Arduino to the system through the level shifter to pins 0/1.

You won't know what you'll receive or can send without looking at the serial output and doing a little tinkering. You don't even know what the serial port does. It could just be for setting up the system.