Best way to chop an onion?
I use two different knives when I dice an onion.  First, cut the onion in half, through the root end (so that each half has a bit of the root on it to hold it together). Next, take a paring knife (the skinny blade is why I use this knife here) and make vertical cuts that go almost all the way to the root.  Next, use the paring knife to make horizontal cuts while using one hand to hold the onion in place. Last, use a chef's knife to make downward cuts to finish the dice.

If you are trying to julienne cut the onion, cut off both the top and root part of the onion and peel it.  Then chop the onion in half vertically and cut thin slices of onion on an angle from the outside toward the middle (about a 10 degree angle should be fine).  I do all of this with a chef's knife.