You should always direct the extinguishing agent from a fire extinguisher at:

Directing the extinguishing agent from a fire extinguisher at the base of the fire is the most effective method for extinguishing flames because it targets the fuel source directly. Fires require heat, fuel, and oxygen to sustain combustion. By aiming at the base of the fire, the extinguishing agent can effectively cool the fuel and remove the heat necessary for the fire to continue burning. This method ensures that you interrupt the fire's chain reaction at its source, increasing the likelihood of successfully extinguishing it.

Targeting the flames or smoke does not address the root of the fire and could allow it to continue burning or even spread. Focusing on the area surrounding the fire could lead to unnecessary use of the extinguishing agent and might not effectively neutralize the fire, leading to potential danger.