Can't comment directly due to rep limit, but I'm not sure Ryan Elkins above is correct. I'm fairly certain both allinase and LFS are found throughout the layers, though the "core" might contain a higher concentration. Certainly there's no gas contained in the central bulb.

There's a couple of basic strategies for avoiding eye irritation:

Avoid breaking cell walls: use a sharp knife

The enzymes and amino acids involved in producing the Onion Lachrymatory Factor (seriously!) are normally contained in the cells, and only become a problem when released in volume. Using a sharper knife will avoid mangling cell walls, creating more clean separations between layers, and reducing the amount of enzymes released.

Slow down the reaction: refrigerate/freeze the onion

I would guess the activity of both enzymes involved here peaks somewhere around room temperature, or maybe a little higher. You want to get out of this optimum range: either freeze the onion, or heat it beyond denaturation. The former is probably way more practical, since heating to denaturation will leave a soggy mess instead of an onion. You may also be able to deactivate the allinase by substantially altering the pH, for example by coating your knife in lye (not recommended) or lemon juice.

Avoid the reaction products: cut underwater or ventilate

The OLF and the reaction intermediaries look to be fairly water soluble, so cutting under running water should take care of them with sufficient flow rate.

I'm not sure what the mechanism behind the common candle suggestion is, OLF is a thial oxide and not very flammable. My best guess is that the rising air draws some of the irritant up and away from the area, but in that case a fan should work much better.

The tearing of the eyes is a result of enzymes that form a sulpherous gas when the onion is cut (concentrated inside the inner core or bulb of the onion) being released into the surrounding air.

You have a few options to avoid this - one would be to not cut through the center of the onion but to extract the "core". This is kind of a pain and means you are discarding a decent chunk of onion, so I don't like it too much.

Another option is to use a fan to blow the gases away from you. A small fan next to you blowing horizontally should do the trick.

You could also wear goggles, although you'd have to leave them on for a while until the gas dissipates from the area.

Another technique is to cut a lemon in half and rub the fresh lemon against both sides of the blade. You'll have to keep "refreshing" the juice coat and your onions will have some lemon juice on them, so this is somewhat limited by that factor.

The best thing to do is very simple: use a very sharp knife and cut them quickly. This causes a minimal amount of the gases in the onions to be released.

As for "tricks", I find that placing a candle by the cutting board to burn off some of the gases released helps for me.

Stick it in the freezer for half an hour first. I just discovered this by accident (I went to get bacon out of the freezer and absent-mindedly put the onion I was holding in the freezer at the same time!) Alternatively, you can put it in the refrigerator, but that's slower, and if you leave it there too long the flavor mellows. Either way, you're making the problematic compound less volatile, so less will end up in the air to irritate your eyes.

As per Alton Brown ^[1]:

• cut near an open flame (e.g. from a gas stove)
• use a very sharp knife

See Good Eats Moment - Cutting an Onion ^[2]

As per my father (addendum):

• make sure the onions are cold
• hang a piece of bread from your mouth. I've never tried it, but according to him it works. YMMV ^[3] of course...

Dicing onions is the act that takes the most time and cutting and so it likely to cause the most tearing. Here is my technique, and I can dice literally 15 onions before my eyes start to tear up.

1. Cut the onion in half, laying the cut sides down. This will keep the gases from escaping while you gut the first half.

2. Slice long longitudinal cuts, leaving the slices attached near he root.

3. Finish your dice with lateral cuts.

4. Put the diced onions in a bowl about 2 feet away.

The trick here is to leave the second half cut side down while you work with the first half. It makes all the difference.

I chop them in half, then run them under the tap, then finish them off. (You can also rinse or soak it after just peeling, but it works better with the cut surface.)

This seems to get rid of most of the crying-chemical for long enough for me to finish anyway.

If you want it to work better, you can also try to keep the knife and your hands wet.

America's test kitchen did a segment on this where they tested out a number of different methods including the various folk remedies that people claim works. The only method that they found to reliably work was wearing goggles (you can even buy special goggles ^[1] specifically made for cutting onions). I don't know if they tested the open flame method or not.

Any method that does not physically prevent the gasses released from the onion from entering your eye simply will not work. The crying is the result of irritation from a chemical reaction when the gasses released by a cut onion interact with your tears (I believe the reaction creates small amounts of sulfuric acid, but don't quote me on that). So you either need a physical barrier around your eyes that keeps the gasses out, or some sort of chemical barrier that will react with the gasses before they reach your eye and therefore prevent them from reacting with your tears.

Of the various answers presented here, the only ones that would seem to have any chance of actually being successful are goggles, a fan (that moves the gasses away from you before they get to your eyes), or possibly an open flame. Of those three, the goggles are the only sure-fire way, as the movement of air is difficult to predict and control.

Cutting them underwater is a little difficult but is the best technique I have tried

Here ^[1] is an article that lists quite a few interesting ways to avoid it. One I think is worth mentioning is to cut the onions under water. I've also read that putting the onions in water for 30 minutes before cutting also helps. Both of these methods would help reduce the compounds that are released when chopping and stop them from going after your eyes :)

Simply breathe only through your nose. Do not talk or open your mouth while chopping. I never cry when chopping onions anymore and haven't in years. I think the bread thing is just a way to keep your mouth closed. (Same goes for holding water or a spoon or a match in your mouth, or chewing gum.)

As implied in some other answers, you want to cut the onion with as few cuts as possible so you are releasing as little of these gases as possible. You want clean cuts.

• Your blade should be sharp. Dull knifes will tear open more of the onion and release more gases
• Use a straight blade. Serrated blades tear and grate and release far more of these gases
• Less motion is better. If you use a hand-held knife or a mechanical chopper that goes straight down, this is much better than using a rotating saw like some restaurants and delis use.

Learn to cut onions faster. Seriously. Unless you're working in a restaurant kitchen and will have to chop more than a dozen (or hundred) of onions, you should be able to chop it fast enough and store them or cook them right away. Then take a few steps back until the gas dissipates from the cutting area.

If I have several to do, I peel them all and cut them in half. Then I do all the chopping at once. You don't need to be a knife master. Just good enough and have a good knife.

For me, wearing contact lenses works perfectly. I can cut onions as much as I like in them, and never cry. It works with all soft contact lenses

Keep your face away from the onion. Seriously! If you just move your head so it isn't directly above the onion when you cut it, the gasses that would normally go into your eyes won't and you won't cry. One way to do this is simply to sit down.

Use a gadget that chops it for you.

They can cut it fast and/or keep the gas away from you eg: Tupperware Choppper Gadget ^[1]

When I worked at subway we had to cut all kinds of onions. This is what worked for us:

Wet a paper towel, fold it (hot dog style), and place it under your eyes and over your nose. You have to make sure you don't lean down too much or the towel obviously falls off. Also, it helps to have a large nose.

Then, if we either neglected to do that, or we simply had to cut too many of them, stepping inside the walk in freezer for just 30 seconds kind of re-sets your tears and buys you another 5 minutes or so of tear free cutting.

Obviously most people don't have a walk in freezer, but i imagine sticking your face in a normal one will work equally as well.

My mother suffers terribly when chopping onions. Her solution is to chop them outdoors. It happens that there's a waist-height coal scuttle a couple of paces from the kitchen door, so she does it on that.

I was taught a method 40 years ago, which boils down to "minimise cuts to the root". It also tries to minimise total time required to cut a whole onion.

Peel your onion before you cut it at all - this is slightly harder than if you top it & slice in half first, but it does minimise total exposure time to cut onion.

Top it, then place it cut face down on your board, so the root is to the top.
From the 'widest' side [no onion is ever perfectly symmetrical] cut from just to the side of the root to the opposite centre - so you've chopped it vertically root to tip but not quite straight, you didn't touch the root.

Lay each side on its flat face. Hold it so the root end is towards your hand.
Make vertical cuts across the curved face, pointing from root to tip. As your knife will be slightly curved, this will still not quite cut into the root. At this stage the onion half is still a single manageable unit, as you don't cut right to the end.
Then make similar cuts at 90° to the first, from top to bottom. Stop when you reach the root & either trim out the last bits, or just discard.

Repeat with the other half.
Of course one half has almost no root at all, the other has almost all of it.

You now have a board-full of chopped onion & the root goes in the compost.

Done. It's quick & easy, even in the hands of a clumsy amateur like me ;)

The world's poorest illustration…

Just one or two is not difficult.

When cutting several I do them one at a time and have a covered bowl at least 3 feet away. Clean up the scraps periodically. Every onion or two I rinse the cutting board.

I've had success with cutting onions near running water.