Once you have sliced, diced or otherwise chopped your onions to the desired size, place in a strainer in the sink. Slowly pour 1 quart of boiling water over the onions to leech out some of the heat and astringency. While warm, I immediately season with salt, pepper and a little vinegar. Now, your not-so-raw onions are perfect!
Some cutting boards, on some counter tops, just slide around as you work. To avoid this, simply place a damp towel under the cutting board. Now it will stay steady and stay put.