Pencil sharpeners: at first thought, sharpening pencil seems like one of those things you wouldn't have to even think about, never mind learn how to do properly but the truth is that if you spend any time coloring or drawing with pencils then you know how valuable the pencils are to you and how frustrating it is when the pencil lead breaks in the middle of sharpening it.
The center of the colored pencil, often refereed to as the lead is actually a color pigment bonded to adhesive agents. This pigment is soft and can break quite easily, especially when you sharpen your colored pencil into a nice fine point.
SO... THE BEST WAY TO SHARPEN A COLORED PENCIL INTO A FINE POINT WITHOUT BREAKING THE PENCIL LEAD IS...
The methods are different for the different types of pencil sharpeners of course. There are electric pencil sharpeners and handheld / manual pencil sharpeners.
Electric pencil sharpeners:
Be gentle with this one, don't apply much force or push the pencil in too much. If you have a good electric pencil sharpener, the motor and blade are powerful and will sharpen the pencil fast so do a little at a time, you can always sharpen a little more but you can never un-sharpen.
Also, sometimes the wax from the colored pencil might build on the blades and clog the sharpener so be sure to sharpen a regular graphite pencil every now and then because the grease that those types of pencils release can help remove the wbuilt up wax off of the blades and keep your electric pencil sharpener working in tip top condition.
Manual pencil sharpeners:
First things is first, is the sharpening blade still sharp enough? Sharp blades can produce a very long and continuous shaving whereas dull sharpening blades produce short segmented shavings. If your sharpener isn't sharp, time to replace the blade or get a new one.
Now that you have a sharp blade here's how you sharpen your colored pencil:
Most of use hold the sharpener in one of our hands, the pencil in the the, and turn the pencil around inside the sharpener but actually you want to do the opposite.
Turn the pencil sharpener around while keeping the colored pencil still.
Don't use too much force, be gentle with it.