Sure, these methods are okay and all, but for my first attempt at writing an instructable allow me to propose what I find to be an easier way of getting that sweet, sweet carbon center out of the also-carbon-based-but-significantly-less-sweet wooden exterior. My proposed solution can be summed up as follows: light it on fire!
Tools and Materials
A means to start a fire (I find that a lighter works best here)
A pencil (one without paint works best, but pencils with paint also work)
A ceramic plant pot plate with a diameter around the same size as the pencil
A knife (a small, easy to handle one works best)
A cup of water (for dealing with things that are hot)
Optional: A candle slightly shorter than the plate is deep
Since you'll be lighting things on fire here, you'll also want to follow basic fire safety, such as keeping something around to extinguish any errant flames or working in a ventilated, clutter free space. As you can clearly see in the first picture, however, I am a terrible example of the latter.
Step 1: Start the Fire!
Light the pencil on fire around the center and then lay the pencil across the center of the plate (see picture).
If you are using a candle:
Light the candle, place it in the center of the plate, and then lay the pencil across the center of the plate such that it cuts across the candle. If the candle is of appropriate height, its flame should light the pencil on fire and keep the pencil lit (again, see picture).
You'll likely have trouble setting a painted pencil like the one I've pictured on fire because initially only the outer layer of paint will burn. With a little diligence, however, you too can eventually light your pencil on fire.
Step 2: Watch It Burn!
Step 3: Extinguish the Fire and Scrape Off the Charcoal
After extinguishing the fire take your knife and start peeling away the charcoal clinging to the graphite. Though most of the charcoal should come off easily, if any big piece doesn't come off almost immediately simply re-lighting that section for a bit should loosen it up. Since the pencil is wet setting a section aflame again will take a few moments, but if you just keep that part in a fire long enough it should soon reignite.