There is a hilarious book called The General Danced at Dawn by George MacDonald Fraser. It is a collection of short stories. One of these is called "Night Run to Palestine" and it starts off with a great little parable about a caboose that came unconnected from the engine while running up a grade. The caboose starts to roll down the hill backwards and goes faster and faster. There are two guys on board and as it accelerates they and get more and more concerned until they decide to jump. Both are injured, one quite seriously.
The caboose meanwhile runs all the way down the hill and out onto the plain where it comes to a stop.
Having worked in kitchens and having spent years now intentionally lighting things on fire in the kitchen and every once in a while unintentionally lighting things on fire in the kitchen, I can say that most kitchen fires are like that caboose. The time it takes to burn off a couple of tablespoons of oil or butter will amaze you but you can usually wait it out.
When something catches fire, the most important thing to do first is nothing. Don't act. Don't even think. Don't let anyone else act. Step back (it is a fire after all) and force yourself to calm down. When you have calmed down, you can start to think about it.
The thing to determine with a grease fire is how much fuel (how much grease or oil) there is. In my case, I knew there wasn't much. So I turned the heat off, moved anything that it might spread to even further away and stood back and watched it go. Once it was obvious there was nothing to worry about, I even laughed.
Okay, in this litigation happy era, a few caveats are required. All this assumes that you have a properly installed stove with a serious vent and have not allowed grease to accumulate on or around the stove or in the vent filter and you don't have cardboard and paper piled all around it and you haven't left a bottle of olive oil or a pound of butter on or near the stovetop. It assumes that you have a fire extinguisher handy and that you know better than to throw water at the the thing or try to carry it out of the house. It also assumes that you have experience with fires—that you have lit them, put them out and even played with fire during your youth instead of practicing the violin and studying all the time so you have some notion of what fires are like.
And if you've never spent time learning to master your emotions you will rapidly learn that it's too late to learn after the fire breaks out.
As with most things in life, it is what you did before there is a crisis that will make the most difference.