How can I troubleshoot and relight a gas fireplace pilot light that has gone out?

To troubleshoot and relight a gas fireplace pilot light that has gone out, first, locate the pilot light assembly and follow the manufacturer's instructions for relighting it. Make sure the gas supply is turned on and the pilot control valve is set to "pilot." Use a long lighter or match to ignite the pilot light while holding down the control knob. Once lit, continue holding the knob for a minute to allow the thermocouple to heat up. If the pilot light continues to go out, there may be an issue with the thermocouple or gas supply that requires professional assistance.