I've been chopping onions for many years, and have tried lots of different methods. This is they way I have come to use after chopping hundreds (if not thousands!) of onions while preparing meals for my family. Some methods have you cutting toward your hand, which I do NOT recommend. This method, in my opinion, is much safer and easier.
Safety Note: As always, be extremely careful when using a sharp knife. Keeping your fingers curved when you are holding the onion steady can help prevent you accidentally cutting yourself instead of cutting the onion! Also, it's actually less likely for you to cut yourself if your knife is very sharp, because then you won't have to apply much pressure to cut. Be careful! :)
Update Note: I think this is a pretty fast way to chop an onion once you get the hang of it, so I timed myself chopping an onion for my dinner preparations. Time from start to finish? 45 seconds! But that was without rushing and with lots of practice. Don't chop faster than you can do safely!
Step 1: Gather Your Supplies
1. Cutting board
2. Chef's knife
I have a large family and often need LOTS of onions for the big cooking I do. Consequently, I try to find the largest onions possible. I've found that Spanish onions are often very large, and one large Spanish onion is sometimes large enough to take the place of 2 or 3 regular size onions ... with less work involved!