The most versatile and budget-friendly extinguisher for the homeowner is a combination of A, B, and C. They are effective on almost any material one would find in a residential house fire.
How to Use a Fire Extinguisher - PASS
To help you remember how to use an extinguisher, use the acronym PASS:
Pull the extinguisher's safety pin.
Aim the chemical at the source of the flames rather than at the flames themselves, standing at least 6 feet from the fire (or as directed on the extinguisher's label).
Squeeze the trigger and hold, keeping the extinguisher upright.
Sweep the source of the flames until the extinguisher runs dry.
Where to Place Extinguishers
The National Fire Protection Association recommends an extinguisher for each floor.
No matter how many you have, nothing is a substitute for the most important tool: a fire plan. Everyone in the family needs to know how to get outside in a hurry, where to meet once outside, and how to call 911.
This Old House has an excellent, six-part "buyer's guide" for residential fire extinguishers. Read the article on the This Old House webpage.