Let's talk about how to create those perfectly square small pieces of onion without crying.
This is the most clear and accurate video I have seen:
I am going to clarify a few things though.
1. Use a serrated knife, like the one in the video.
2. Imagine the onion is a planet. The root is south pole and the head is north. When you cut it in half, it is from north pole to south pole, and NOT along the equator.
3. When you are cutting one half into slices, leave the last ¼ from the narrow end uncut.
4. Cut the onion vertically, not into wedges
The angle of the knife can be misleading, but it is so I can show you how my fingers are curl up. The knife should otherwise be perpendicular to the cutting board.
5. When it is time to cut the onion horizontally, make sure you know where all your fingers are. If you are doing this for the first time, keep all of your fingers up. It might make the cutting a little messy, but at least you wont' cut yourself.
6. Thickness is up to you, but I prefer cutting it in quarters.
7. Again, leave the end uncut.
10. Time to cut it into the final product. Again, thickness is determined by personal preference. For perfectly square pieces, you want to cut at it the same width as your previous cuts.
11. The knife should be perpendicular to the cutting board.
12. All your fingers should be curl up behind the knife. All your fingers should be applying pressure to secure and stabilize the onion.
13. Don't put the onion through towards the knife. Instead, move your hand and knife backward to the uncut part. Your knuckle should always be against the side of the knife.
With practice, it will take no more than 30 second to cut an onion. This method can also be used on other round product, such as shallots, tomato, etc. This is how chefs is able to create tiny little pieces of food out of something that is round.