The Fire Arrow was a relatively simple weapon. The arrow head was wrapped in cloth and dipped in sesame oil, and then covered in lard and was ignited prior to firing.
The Art of War lists five methods of using fire in an attack: against an enemy camp, against enemy stores, against supply lines, against arsenals, and against enemy soldiers in the field. It was mostly used during dry seasons, when the fire would have spread the most quickly.
Historically; fire arrows were specifically used to burn buildings and towns instead of against humans. As the show pointed out; the penetration and lethality of the arrows are weaker compared to ordinary arrows.
The Huo Chien was tested against the hand cannon. When an area was prepared for it's use it was shown to be highly effective, however when used against a single opponent it proven to be highly ineffective. The wrappings around the arrow head keep the arrow from penetrating deeply enough to actually cause serious harm, and the force of the impact caused the flame to go out. It also proved to be counter-productive, as the heated arrow tip cauterized the small wound it did inflict, making it bleed less.