If your pencil breaks and you really need one, this is how you sharpen a pencil with a knife.

[edit] Steps

Using a knife to sharpen a pencil.

Hold the pencil, pointing the lead tip away from your body, with your non-dominant hand. (If you are right-handed, hold the pencil with your left hand.)
Hold a knife or blade in your dominant hand.
Place the blade about an inch above the lead at a 45 degree angle. Point the blade away from your body!
Apply light pressure and stroke the blade outward and down.
Rotate the pencil with each stroke to allow for maximum lead exposure.
Finish by cleaning up the pencil shavings. (Do this over a rubbish bin to minimize cleanup.)
Wipe the blade clean of lead and debris.

[edit] Tips

This is only suggested if you do not have access to a pencil sharpener.
Sharpening a pencil with a knife can be handy for carpenter's pencils and other odd shapes or sizes that don't fit in a sharpener.
If you really need to, a pair of scissors works well, too. Simply open the scissors all the way and use one blade to sharpen the pencil.

Be extremely careful. It is quite easy to cut your fingers while using a knife to sharpen a pencil. Watch out for other people!
Do not use this pencil sharpening method at a school. Knives are not allowed!