For trouble-shooting an existing system, the absolute minimum is basic hand tools like wire-strippers/crimpers (most of this is very small gauge wire), screwdrivers, and some means to test for continuity on a circuit. This is all 12vdc, except for the 16vac transformer, and you can do a surprising amount with an automotive test light, but having an inexpensive Volt/Ohm/Milliamp Meter, and learning to use it, can save you a world of headaches and frustration. For more than the basics, like installing or modifying a system, you will need drills and bits that can go through aged wood (drilling even a 1/4 inch hole through the thickness of a old door header will push most consumer grade tools to their limit). You may find a few trips to the tool rental store in order.

Source: http://forum.doityourself.com/electronic-alarms-home-security-devices/203784-alarm-forum-faq-please-read-before-posting.html