A car's fuel pump relay turns on the fuel pump when the motor runs. When a relay is defective, it is usually because of a bad coil or bad connection. To check both operations, remove the relay by pulling it out of its socket. Consult your owner's manual or a service manual to find the location of your fuel pump relay. Familiarise yourself with the operation of a multimeter, or ohm meter, before beginning the job.
Set the multimeter up to read ohms. The ohms scale looks a little like a horseshoe.
Touch the meter leads together to test the multimeter. You should read zero ohms.
Touch the test leads across the coil of the relay. You should read about 70 ohms. If the meter reads zero ohms, the coil is shorted and your relay is bad. If the meter reads infinite ohms, your coil is open and the relay is bad.
Connect one of your test leads from one side of the relay coil to the chassis ground.
Connect the other test lead from the other side of the coil to the vehicle's battery. The relay should operate and you should hear or feel a click.
Connect the multimeter across the common (C) and normally open (NO) contacts of the relay. The relay should read zero ohms. If not, the contacts are not making a connection and the relay is bad.
Be careful connecting your test leads to be battery. If you short the battery positive lead to ground, you could get a tremendous spark.