What kind of alarm do you have?
I change the battery on mine not to long ago. The battery is in the main alarm box in your house (under the stairs maybe). When you unscrew the cover the alarm will go off, enter the alarm code on the keypad will stop it.
Then just take out the dead battery and replace with a new one.
Obviously make sure you get the exact same type of battery.
Find out your alarm type, do a bit of searching on the web about changing batteries on it and if you don't feel comfortable doing this get an electrician in. It is a very small job.