Unplug the lamp and take out the bulb.
Connect the test probes to their appropriate receptacles on the multimeter. Red goes to the positive slot, and black goes to the negative, marked "Volt" and "COM."
Set the dial on the multimeter to measure ohms, or resistance. This is marked with the Greek letter omega.
Touch one end of the probe to the metal strip at the bottom of the socket, and touch the other probe to the side of the socket. You should get a nonzero measurement; if you don't, it means that the lamp's circuit is broken or shorted. A short circuit is dangerous and can cause a fire.
Touch the two prongs of the lamp's power cord using the same method -- you should get approximately the same result.