Above and below are the diagrams of the electronics that will interface the alarm system sensors with the Raspberry Pi. The first diagram is a conventional electronics schematic and the second is how you can build the circuit prototype on a bread board.
We have shown two identical circuits representing two contacts in your alarm system. You can repeat the pattern as many time as you like, but within the limitations of the number of available IO ports on the Raspberry Pi.
The Magpi Magazine (www.themagpi.com) is an excellent resource for learning electronics on the Raspberry Pi. Refer issues 2 & 3 for deeper explanation behind the electronics shown on this page. The diagrams below are adaptions of the circuits in Magpi Issue 3.
The switches in the diagrams are the door contacts or the motion sensors of the alarm system. Door contacts (known as reed switches) are the easiest to work with and probably a good starting point. A reed switch has two halves, one half goes on the door and the other half goes on the door frame. The half on the door frame contains a magnet that holds the switch closed when the door is closed. When the door opens the magnet is no longer holding the switch closed and the circuit is broken triggering the alarm.
For more detail: Alarm Electronics