Putting out fires means to put out the fires. But what if it's a just a spark or at the kindling stage, and you put it out, is there a word for that?

douse 1. TRANSITIVE VERB If you douse a fire, you stop it from burning by pouring a lot of water over it. The pumps were started and the crew began to douse the fire with water. 2. TRANSITIVE VERB If you douse someone or something with a liquid, you throw a lot of that liquid over them. They hurled abuse at their victim as they doused him with gasoline. collinsdictionary.com

quench transitive verb 1a: PUT OUT, EXTINGUISH b: to put out the light or fire of quench glowing coals with water. m-w

You can extinguish a small fire with a fire extinguisher, for example. The fire department extinguish larger one. Douse, to my mind, is apt for small fires -- perhaps a pan catches fire while cooking. It connotes the use of a quantity of water. You can douse a campfire with water. It can be used for large fires as well, however.

Instead of water, you can use a lid or a towel to smother a kitchen fire.

smother verb (used with object) to stifle or suffocate, as by smoke or other means of preventing free breathing. to extinguish or deaden (fire, coals, etc.) by covering so as to exclude air. dictionary.com

Getting smaller, some folks like to show off and snuff out a candle using their fingers; others simply blow a candle out. You can put out a fire as well. The phrasal verb, as you might expect, is less formal than extinguish, which we get from Latin.

"Humans cause nearly 85 percent of wildland fires in the United States, according to the Forest Service. One of the culprits? Campfires that aren’t completely out. Letting your post-s’mores logs burn down unsupervised isn’t safe—you’ve got to douse them with water until the coals are cool." The Right Way to Put Out Your Campfire

"If you need to add water to douse any embers, do so slowly, and sprinkle it on rather than soaking the fire and surrounding soil." Camping for Dummies