I have an 1988 Buick Regal Custom that will not start. Why would it be doing this?

Check to see if there is any codes (if your car is equipped with an OBD II port). Check to see if you can "hear" the fuel pump running in the "Key On, Engine Off" position (IF you just did this, give it time to allow the fuel pressure to release before trying again). If you hear the fuel pump come on, then my next thought would be check the ISC (Idle Speed Controller) or IAC (Idle Air Controller) to see if they are operating correctly. Which ever one your car has, the intent of the unit is to control the RPM's of the car until it warms up by regulating and monitoring the fuel/air ratio.

Bad fuel injectors