Fuel pump fuel filter?

You ask where to start. I recommend purchase of Chilton's Camaro/Fire Car Care Manual available on-line or @ your local parts house. While you are there, pick up a new fuel filter if it has been more than a year since service.
The manual will have the info you need, and it is quite comprehensive, although a little hard to get used to (like most Chilton's Manuals). A malfunctioning EVAP purge valve or vacuum leak for same, could also be an item to check. Fuel pressure regulator, fuel injectors, or something simple, such as a blown fuse. It's covered in the manual and if you are mechanically inclined, you might consider the purchase of an OBD ll code reader for GM cars. That will narrow your search to a specific component or signal path. Good Luck! :)