The outer most layer of onion is often not that good as it can still get pretty tough /papery near then ends. I typically cut the tip of the root and stem ends off, then cut the onion in half with the skin still on, then cut just though the skin and outer most later lengthwise (from root to stem). I use the tip or heel of the knife to "flip up" or start skin away from the onion along the line that I just cut. This way you are only trying to remove 1/4 of the skin at a time and it's easier for the skin to invert / turn inside- out come off in one piece when it's only in a 1/4 section vs a 1/2 sphere.
One other trick that I've seen is to not trim the stem-end off before halving the onion and to use the little "point" or tab of skin at the tip as a place to grab and start the peeling.
I've also heard that microwaving for a few seconds or placing the whole onions in a hot oven helps to separate the skin. I haven't tried that, but it only really seems like it would be a time savings if you where doing A LOT of onions all at once... and it would probably make the tear-gas more volatile.