What can cause my 2002 Toyota Celica to die on its on after completely starting?

Does if run ok if you give it a little gas after starting then die after gas pedal is release? Or die anytime that it returns to an idle? If so I would suspect the throttle body needs cleaning and or the idle air control valve is going bad.

Agreed. But please answer that, about does it run with a little throttle as he asked. That will help us.... Good mornin' dandy

If I push the gas it tries to stay started for a couple of extra seconds but dies out still.

Mornin DavidH25. I like the new avatar. Seems that problem is common on your model car. Found several answers leading to MAF cleaning, iac cleaning or replacing, vacuum hose issues and cleaning throttle body. These might be a good places to start. How long since your last major tune up( plugs, wires, air filter, ect)?