How can I troubleshoot and relight a malfunctioning fireplace pilot light?

To troubleshoot and relight a malfunctioning fireplace pilot light, first check for gas flow and ensure the gas valve is open. Next, follow the manufacturer's instructions to relight the pilot light using a long lighter or match. If the pilot light still won't stay lit, clean the pilot assembly and thermocouple. If the issue persists, it may be a more complex problem requiring professional assistance.