Cut the skin and fat into even-sized small pieces. The exact size doesn't matter much, but approximately ½ - 1 inch in diameter.
Heat a large-enough (depending on how much skin and fat you are rendering from) non-reactive pot or skillet over a high flame.
Add all of the fat and skin pieces, and turn flame down to medium low. Stir.
Stir periodically -- don't let things stick to the bottom. As the fat begins to render out, there will be a lot of liquid in the pot or pan. Much of this is water, that you will want to let boil off. Adjust heat so that there is at least small bubbles, and you can see steam rising out.
Once the liquid is starting to turn yellow (it will be more mild at first, like the color of mustard powder), raise the heat to medium high.
Add the onion to the pot and stir.
Patiently let nature do its thing. The heat will render the fat out as liquid, and evaporate the water. Keep stirring periodically, but beyond that, just let it go. This will take a few hours. You clearly don't need to watch or stir it constantly, but don't forget about it either!
Once the liquid in the pot has reduced to mostly fat that is a deeper yellow in color, and once all of the skin pieces have shriveled up from losing most of their fat, it is time to separate the wheat from the... or better yet, the schmaltz from the skin and onions.Pour through a strainer into a large bowl. If you pour straight into a glass jar, you run the risk of cracking the glass due to the temperature and thus losing your golden treasure. Shake the strainer holding the solid pieces to make sure you let all of the goodness drip out. Return the skin to the pot/pan over medium flame to render out any remaining fat. Once it has all been released, and poured through the strainer, you're done. Let the schmaltz cool, and then pour into a jar. You can keep it in your fridge for at least a week, if not more.Alternatively, freeze the schmaltz either in individual portions or in a plastic container from which you can scrape out what you need each time.