Look at the markings on top or side of the relay case and locate the two control circuit terminals, which connect to the relay's coil, and the two power circuit terminals, which let electrical current pass to the fan. If your fan relay does not have markings on it, you will have to consult the cooling fan wiring diagram found in your vehicle service manual. See the Tips section at the bottom for more information.
Connect the leads of an ohmmeter to the power terminals on the relay. Set the ohmmeter to the lowest range. You should read infinite resistance. If you read any amount of resistance, the relay contacts are stuck closed and the relay should be replaced.
Hook one end of a fused jumper wire to one of the relay control terminals and the other end to the positive terminal of the car battery. Attach the end of a regular jumper wire to the other terminal of the control circuit on the relay and touch the other end to ground on your vehicle. As you touch ground with the jumper wire, you should hear a click sound coming from the relay. This means the relay contacts are operating normally. If you do not hear the click sound, replace the relay.
Leave the jumper wires connected to the relay control terminals if you heard the click sound in the previous step. Using your ohmmeter as described on step 2, check for continuity at the relay's power terminals. Now you should read zero resistance. If you get infinite resistance from the ohmmeter, the relay contact points are not letting electric current flow through. Replace the relay.