Horn Beep

This setup shows how a relay can be hooked up to make the car horn beep when the alarm goes off, using the parking light flash output off the alarm. The relay switches polarity from positive to negative, acting as a polarity inverter.

Note:  It is assumed that the alarm is either using another relay to make the actual parking lights blink, or there is a diode at the connection with the lights.  If not, every time the car's lights are turned on, the horn will sound!
Another way of hooking up the horn beep, is to connect the 86 terminal of the relay to the alarming output of the alarm (if it has one), or maybe to the starter disable output of the alarm (if negative).
  

Starter Interrupt

Find the starter (crank) wire at the ignition switch and cut it.  The normally closed (87a) terminal of the relay is used.  When the relay is off, the starter wire that has been spliced to the relay will conduct, since there is a continuous circuit.  When the alarm is turned on, and the relay gets a negative (ground) input at terminal 86, nothing will happen.  However, when the car is cranked, the relay will immediately click, cutting off the starter wire.

Note:  Same results could have been achieved, just by simply hooking up the 85 terminal of the relay to a constant +12 volts source.  Problem is that the relay will be activated all the time when the alarm is on, drawing current from the battery.