Without knife skills, how can I quickly and accurately dice vegetables

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 California Avocado Commission recommends this (safe but wimpy - see below for a better way) three-step process:

1. Start with a ripe avocado and cut it lengthwise around the seed. Rotate the halves to separate.
2. Remove the seed by sliding the tip of a spoon gently underneath and lifting out. The other common seed-extraction method - striking the seed with a knife and twisting - requires some skill and is not recommended.

3. Peel the fruit by placing the cut side down and removing the skin with a knife or your fingers, starting at the small end. Or simply scoop out the avocado meat with a spoon. Be sure to sprinkle all cut surfaces with lemon or lime juice or white vinegar to prevent discoloration.

   

Source: California Avocado Commission

Notes:

• Another (and my favorite) way to remove the pit is by holding the half with the pit in one hand and striking the sharp edge of the knife used in step one into the pit, then twisting to remove. This is the "pro" way to do it, but takes a little practice. The video Nate referenced in the comments shows how to do it, it's not that hard.
• If you're going to be chopping the avocado up, you slice it up using the tip of the knife still in the shell, then scoop the sliced avocado meat out with a spoon.