Most often, simple fire extinguishers use sodium carbonate and dilute sulfuric acid to produce carbon dioxide, that extinguishes fire. small pouch carries the acid within a matrix of sodium carbonate. The pouch prevents the acid to come in contact with sodium carbonate outside. When the bottle is shaken, the two chemicals come in contact with each other, liberating carbon dioxide and water droplets that extinguishers.
Another type of fire extinguisher contains compressed Carbon Tetrachloride in it. When the nozzle is pushed, an aerosol of carbon tetrachloride is liberated that suppresses and extinguishes fire. This type has a major advantage that it can extinguish fires of oils, electric circuits, etc.
Other forms of fire extinguishers use forced water to extinguish fire.