Check whether the pilot light is on. If it goes out repeatedly, that may be the first indication the thermocouple is bad. If the pilot light is off, relight it according to the directions printed on the hot water heater. The sequence usually involves turning the control knob to "Pilot," lighting the pilot light with a match or lighter and holding the knob down for at least 60 seconds to make sure the thermocouple warms. Let go of the knob. If the pilot light goes out, the thermocouple could be the problem.
Shut off the pilot light if it's on. Simply turn the knob on the gas control knob to the "Off" position. Turn off the electrical power to the water heater as well. Either unplug it or shut off the breaker that controls the water heater.
Set the multimeter to detect ohms, at the lowest ohm setting on the testing device. Multimeters can check resistance and voltage, so make sure the leads are connected to the right ports for checking resistance. The ports will be labeled.
Touch one probe to each end of the thermocouple. A zero or very low ohm reading indicates the thermocouple has no short along its length. If a short were present, the multimeter would show a higher ohm reading. If it does, replace the thermocouple.
Set the multimeter to measure the voltage by switching the leads to the ports marked for voltage tests. Set the selector switch to detect the lowest voltage readings possible on your particular multimeter.
Place one probe on each terminal of the thermocouple, then hold the end of the thermocouple between two fingers. The warmth your fingers generate should be just enough to register a slight jump in voltage on the multimeter. If no voltage registers, the thermocouple is not functioning correctly and needs replacing.