One of the most effective approaches in fire extinction is removing the heat. Thus, cooling with water is one of the most popular methods. The heat generated by the fire is absorbed by the water. This remains effective as long as the water can still absorb the heat.
However, it is important to know that water should never be used in fires involving electricity, cooking oils/fat, grease and other flammable liquids.
Starving the fire from its fuel source is a different approach. When fire runs out of flammable materials, it will eventually burn out itself. For bonfire in the open when it is not in contact with any other wood or dry grass will ultimately lose its blaze. In a gas fire, it will immediately extinguish if the gas supply is cut off. The same method is applied to your gas stove or bunsen burner.
The third approach involves the last element in the triangle, oxygen. Smothering is a technique where oxygen is removed from the equation. An example of this is using a fire blanket in a frying pan blaze to reduce the oxygen level below 16%. Covering a candle with a glass is also an example. The fire burns out all the oxygen inside the glass creating a vacuum.