Remove the entire burner pipe and pilot tubing, along with the wire that attaches to the thermocouple. There are two captive fasteners on the bottom of the gas valve to loosen and you'll also have a couple of sheet metal screws to remove that hold the burner assembly in place. Do not cut the wire. Do not adjust any of the screws on the gas valve. That is above your paygrade and will probably mess things up.
After you have the burner assembly in your hands and removed from the water heater, look on the end of the burner pipe. There will be a small brass orifice there with hex sides. Remove this orifice and soak it with carb cleaner, dilute ammonia or other cleaner. Blow compressed air backward from delivery direction through the orifice. You should be able to see daylight through the small hole.
Clean out the burner tube and lightly sand the thermocouple (the cylinder on the end of the pilot tube where the wire attaches). Reassemble, making sure the thermocouple is in the path of the pilot flame. Try ignition and adjust the air mixture baffle (the steel clamp that is attached to the burner tube with a machine bolt and nut) until flame is nearly all blue. You should have no soot after this.
You could also just do the last step, adjust the air mixture baffle, but that water heater is in sore need of a good cleaning.
