First things first: A day ahead of time, check your fire extinguisher's pressure gauge. If it's low, contact your local fire department to find out where you can get it refilled and place it prominently in your kitchen. While it may be helpful to have a small extinguisher near the stove while you're cooking, make sure you've also got one by the door; you should not have to risk burns just to reach your extinguisher in the event of a fire.
The other thing you need to keep handy is a large pot lid and a heavy-duty oven mitt. Stash both of these within arm's reach of the stove in case you face a grease flare-up while you're cooking. Whatever you do, don't try to put out a grease fire with water; water will only spread the fire and make it more dangerous. The National Fire Protection Association
recommends first turning off the burner to eliminate the heat source. Then throw on the oven mitt, grab the pot lid, and smother the flame. Keep the lid on the pan until it's completely cool, to keep the fire from restarting. For more ways to be prepared for a cooking fire, see our guide on Stovetop Fire Safety