there should be a large wall wart power supply... this may likely be near the "brain" or alarm panel (in closet, or basement) just unplug that... but inside of that alarm panel there is also a back up battery, you should also disconnect the back up battery, or the alarm may see that the power was "cut" and trip...
alternatively if you can not find where the wall wart electrical transformer is located (sometimes it is installed away from the panel, as to not make it as easy to disable, or because there was no power outlet nearby) the contacts on the circuit board inside the panel are labeled... the writing is small.. but if you look real hard you should see 2 wires should say something like power, pwr, DC, and may include a + and - to distinguish which one is which... if you did not remove the transformer from the outlet, remember, when you remove these wires from the circuit board there is still power going thru then (low voltage) so you should cut the exposed wire and tape the ends... ideally you should really find where that wall wart transformer is located...
the wire on the back up battery in the panel should just slide off...
(EDIT) if your phone line is connected to the alarm, removing your phone line from the alarm box will likely also remove the dial tone to your phone jacks in your home... if the alarm was wired to the telephone line properly, the wire runs from the NID to the alarm, and back to the NID where it connects to your inside wiring... so if you remove the phone wiring @ the alarm panel, you should splice the TEL IN and TEL OUT, or TEL CO and TEL STA together...