When combining heat, fuel and oxygen we create a process or chemical reaction that is called combustion. The process only works when you have three elements present. Oxygen fuel and heat. The chain reaction causes the flame. The flame is energy released to the atmosphere.
Best example is the humble camp fire. You place kindling with larger pieces of wood above. Place a heat source a match and lighter and blow on the small part that is burning (the kindling) till it gets larger. Almost always the struggle at the beginning is to add oxygen. So, we get down on our knees and blow into the kindling.
One point to make is that if you start with a lit pile of coals from another fire instead of a match it is much easier to get the fire started. Or get left over coals that are out and add a bit of BBQ starting fluid and light it. This small pile of embers will get your fire going.
To successfully put it out most of the time we pour water to reduce heat and limit air. It goes out by itself if it runs out of fuel.