The fuel pressure regulator regulates the pressure of the fuel in the fuel lines to the proper level. If the fuel pressure regulator is defective the fuel pressure supplied by the fuel pumps may be too high (or sometime too low) resulting in the incorrect amount of fuel being injected each time the fuel injectors fire. Normal symptoms would include a vehicle that is running rich with black smoke coming out of the exhaust, decreased fuel economy, and potentially gasoline in the oil.
The fuel regulator is a small cylindrical object, normally in the engine bay, with a vacuum hose running to it. It will also be attached to the fuel lines somehow, either via hoses or by direct connection to a fuel rail. If the vehicle is equipped with a test port you should be able to test the fuel pressure regulator's operation by attaching a gauge to the test port. With the gauge attached and the car running take a fuel pressure reading. If you have access to the manufacturer's information you can compare this to the expected value, otherwise turn off the engine and disconnect the vacuum hose from the regulator. Inspect for any fuel inside that vacuum hose as this can indicate a leaky diaphragm in the regulator. With the hose still detached start the car and take another fuel pressure reading. The fuel pressure should have increased quite substantially with the vacuum hose removed (by around 10 or more PSI), otherwise there may be a leak in the vacuum hose or the regulator may be defective.