I have slaved over bins for too long with a blade paring back the wood until the lead breaks. After ten or fifteen minutes all you have left is a reasonable point on a short lead on a short pencil and a bin full of shavings.
Would you like to get a deadly point in about ninety seconds? Try this technique:
This is 180 grade sandpaper, but any grade will do fine. Use thumb and index finger atop the head of the pencil and stabilise the back of the pencil with the heel of your hand. The blue the blue pencil is a rest to maintain a constant grinding angle, also on the sandpaper to stop it skidding away. As shown in the finished points at top of the photo l like to grind three faces to give me nice flat edges for sketching and a great point for detailed work.
Tap the dust into the bin and your done.
The same technique can be used with color pencils or pastel pencils, though go more gently with these.