Find the main alarm panel. It's usually hidden in a utility room or in the attic. It measures about 1 foot by 1.5 feet and is usually a pale color.
Open the alarm panel. You will recognize the battery because it is plugged to red and black wires.
Unplug the old battery and plug in the new one. The "BAT" indicator may not go out for several hours until the system performs an automatic test. This is normal.