When you're ready to clean your gas range, turn off the gas and unplug the range.
The eyes of the range tend to get dirty fairly quickly. To clean them, lift out the grills and drip pans and wash them in soapy water.
The burners are removable for cleaning, too. You may need to loosen a nut before pulling the burner out of the range. Soak the burner in a mild solution of liquid detergent and water, then clean it with a toothbrush. While you have the burner out, check the internal drip pan, and clean it if necessary.