Taking the concept of the fire triangle a little further, one can see the ideas behind most wildland firefighting techniques. If one leg of the triangle is eliminated, the triangle collapses and the fire goes out. Eliminating that one leg is what firefighters attempt to do to control or put out a wildfire.
Putting water on a fire is probably the first thing that most people think of when they think of putting out a fire. Water cools the fire, thus removing or weakening the heat side of the triangle, and can prevent air from getting to the fire, weakening the oxygen leg of the triangle. If water is applied correctly, the fire goes out. Water is applied to forest fires in several different ways. Helicopters may be used to drop water from buckets onto hot spots inside a fire's perimeter. Air Tankers, airplanes that drop a mixture of water and fertilizer can be used. Hose lays, a network of hoses, pumps, valves, and nozzles may be used to get water where it's needed on a fire. Water can be carried to the fire on 5 gallon rubber backpacks carried by firefighters and applied with the attached hand pump. These containers are called Fedcos, bladder bags, or the more common name piss bags. No matter what the technique used, water puts out a fire by eliminating heat and oxygen.
Dirt can also be used to extinguish a fire. The same concept applies when using dirt as when using water. The dirt removes some of the heat of the fire, and also prevents oxygen from getting to the fire. Soil can be thrown on flames and hot spots using shovels, or can be mixed with hot embers using shovels and pulaskis.
The third concept that I'll look at here, is the removal of fuel in attempting to put out a wildfire. This can be accomplished by digging a fireline, which is a trail with all the vegetation and other fuel cleared from it. When the fire burns up to the fireline, there is nothing more for the fire to burn, so it goes out. The width and type of fireline or fire trail to be dug is determined by the observed and predicted fire behaviour. Firelines vary from 2 feet in width to several hundred feet wide. They can be created by fire crews using hand tools or bull dozers. A common way that firelines are used in putting out forest fires is to dig the line a ways ahead of the fire, then backburn the fuel between the fireline and the active fire. Backburning is igniting the fuels and eliminating them in a controlled manner. This is a very effective way of breaking the fuel leg of the fire triangle.
So in recap, wildland firefighting techniques attempt to extinguish wildfires by eliminating one or more legs of the fire triangle. When that happens, the fire no longer has what it needs to burn, and the fire goes out.