Call your monitoring facility and tell them you want to place the unit in "test" for an hour (during test they can still see any alarms but they will not respond to them).
Disconnect the power from your system. The power supply may be secured with a retaining screw; remove it and unplug the system.
Press the tab on the top of the panel and swing the panel down from the base plate, if your unit is wall-mounted use a regular screwdriver to press the tab.
Unplug the connector going from the battery to the system.
Remove the cover from the battery compartment (which is located on the base plate). Note how the wires (red and black) are routed and remove the battery.
Put the new battery in the battery compartment. Replace the cover making sure you tighten the retaining screws fully.
Plug in the new battery. Route the wires through the holes the same way the old battery wires were routed. Swing the panel up and snap it closed.
Plug the unit back in and tighten the power supply retaining screw.
Make sure your system is operational. Call your monitoring facility and have them take the unit off of test.