Lay the onion on the side with the stem chopped off and slice it in half.
Start to peel the skin off of the onion, throwing it away in a refuse bin. If using half an onion, leave the skin on the unused half intact and wrap it.
Start to chop the onion vertically using the flat side of it as a base. Do not cut all the way through.
Rotate the onion and start chopping it in the other direction. For smaller pieces, make the cuts close together.