How does the anti-theft work on a Oldsmobile intrigue 1999?

I assume you are referring to the radio? It has a four-digit security code that the owner can set. When the power to the radio is disconnected, (either because of battery removal/failure, or because the radio was removed) the radio will "lock" and the four-digit security code must be entered again to unlock the radio, before you will be able to use it again. If you do not know the security code, you will need to take the car to a GM dealership, and they will have to unlock it for you.