There are several things you may consider when checking your fuel pump for problems. Any number of things can go wrong with an overused fuel pump, and discovering the severity of the issues along with the causes can help you prolong the life of your pump and vehicle. To perform proper fuel pump troubleshooting, it is generally a good idea to start with the most basic things and work your way up to more severe problems. Check each part of the pump carefully to ensure that you don't miss something obvious.
Start by opening the gas cap, or removing it entirely, depending on the vehicle. Have someone else turn the ignition without starting the engine. Listen very carefully for a rhythmic vibrating sound coming from the fuel tank. If you hear this sound, your fuel pump may be good working order. If you don't hear it, continue fuel pump troubleshooting to discover any underlying problems.
Check the fuse panel under your dashboard or in the engine compartment under the hood. There should be a circuit box with a fuel pump circuit fuse. Make sure that no wires are corroded and that everything is properly connected. If not, you may have to replace wires or the entire fuse. Should you have to replace any parts, do so and check the fuel pump again.
For proper fuel pump troubleshooting, you should also carefully look for any tears, holes, or worn spots in your fuel hoses and lines. Replace the defective parts and try the fuel pump again. If all hoses are in good condition, then find the fuel pump relay by checking under the hood on either side or as a system of relays toward the back. Once you've found it, inspect the wires by having a friend turn the ignition without starting the engine. Use a test light to note the voltage coming from the wires.
During this phase of fuel pump troubleshooting, you may be able to jump the relay in order to allow battery voltage to run through the system. Repeat the first step to listen for proper fuel pump functioning. If the pump works now, then you may have to replace your relay. You could also check the connection between your relay and the fuel pump by using a test light and having a friend turn the ignition without starting the engine. This will also let you know if you need a new relay, fuse, or connection.
You should also check the connections located directly at the fuel pump for corrosion or wear. If there is none, the final step in fuel pump troubleshooting is to remove the fuel pump and apply direct voltage to it using your car's battery. Should the pump still not work when applying direct voltage, you will likely need to purchase a replacement fuel pump.