Everyone has their own way of cutting an onion it seems like, but I am going to show you what I think is the best way. Using your cook’s knife is the ideal knife to use here.
First, place the onion on a clean cutting board with your knife ready. Slice off the tip of the onion, the opposite side of the roots. Then, you will want to cut off the roots, but leave as much of it intact as you can. By leaving most of the roots intact, you avoid the juice of the onion running and you will not have the urge to cry.
Then, cut the onion lengthwise (crossing over the tip and the root). Then peel off the outer layer of skin.
You now have two clean halves of an onion. Place the roots facing away from you. Then you will want to start making incisions into the onion from the tip toward the root. Cut all the way almost to the the root, but do not cut completely through the root. Repeat this process beginning from one side, working your way the the other side.
This next step is OPTIONAL because of its difficulty and risk of injury to beginners. If you want smaller pieces of onion, you will want to make an into an incision or two (either is fine) that intersect the previous cuts from a side view. It is very important that you hold the onion by pressing your palm down on the top of the onion. Do not let your hand be in the path of your knife! Again, you want to stop just at the root.
Here is the final and most exciting step! The last set of cuts should be fairly obvious now. Make a series of cuts that intersect the first set of incisions when looking from a bird’s-eye view. Cut all the way until reaching the uncut portion of the root.
Congratulations! You have now have a pile of diced on your cutting board!