The Firefighter vehicle mission is available from the beginning of the game and requires you to have a Firetruck. You can easily get one by starting a fire anywhere there is roads. Some good spots to perform the mission are Angel Pine and Los Santos. What you need to do for this vehicle mission is put out fires with the hose on the top of the truck, which is controlled by the Circle button, B button or the Left Mouse Button. The right analog stick or mouse will control where you're spraying the water.
The objective of the Firefighter mission is to put out the fires of vehicles and people. The first level starts out with a single vehicle on fire and as the levels progress, you will get more vehicles and even people, up to a max of 3 in a car. Remember that the Firetruck won't catch on fire, so you can get close in order to put it out. Also, the Firetruck cannot be repaired via the Pay n' Spray, and you cannot leave it once you begin the mission. For completing level 12, Carl Johnson will become fireproof.