Well, depends on what vehicle. For instance, the older ford pickups had a booster pump that bolted on to the frame and another pump in the tank. I have seen the pump in the tank go bad and the booster pump still good. It would start hard and die later. The booster pump would suck fuel and then loose prime. Generally though, it would be like the other answers said. There is generally a pepcock on the fuel rail that you can check the fuel pressure and see what its runnin.

Turn key on and listen for fuel pump to run for 2-4 seconds then stop running.If you don't hear that,the fuel pump isn't working.Check the fuse.Locate the fuel pump relay and listen for it to click when key is turned on.If it doesn't click,the relay may be bad.The easiest way to check is to find another relay closeby in the panel and borrow it to insert into the fuel pump relay terminal.The part number on both relays has to match or it won't work.If this doesn't fix the problem,remove the relay and test for 12volts at relay connecter.If voltage isn't present,there is a open or short in wiring between relay connecter and computer or connecter and ignition switch.If 12volts was present and relay is good,remove wiring harness at fuel pump and test for voltage.If 12volts is present,the fuel pump is bad.If 12volts isn't present,there is an open or short in wiring harness.Check the terminals for corrosion too.Now for a pump check.The pump has to work in order for this test

A turn over - no start condition

no fuel.. they either work or dont.. if you can have a buddy jump in the driver seat and turn the key and you listen with the gas cap off your ear right next to it you should hear a buzzing if not fuel pump isnt working..

Here is a video that will help you diagnose your fuel pump.