There are two methods for extracting a broth from a set of ingredients: stovetop and crockpot. If you want a quick broth, you have to make it on the stovetop, and because you want it to be quick, it mustn't contain any fat, or any fat to speak of.

So the routine for a quick broth is:

Put nonfatty ingredients in a pot, cover them with water (or with some previously extracted broth, simmer them as long as you can.

If at the end of the available time the ingredients still have a good deal of savor, you might use them in a second broth.

If you want to make a broth from fatty ingredients, then it really has to be slow. The how-to columns of the food magazines describe numerous ways of defatting quick broths, ways involving shallow spoons, ice cubes, paper towels, slotted spoons and sieves kept in the freezer, skimmers, old pillowcases, newspaper, cheesecloth, bulb basters, and cold shoelaces. A special vessel for defatting broths exists. It's called a fat separator or a gravy separator. It's a pitcher with a low spigot, and it works because fat is lighter than water. The fat rises to the top of the main body; the spigot draws from the broth below the fat. And indeed, if your broth is to be used where some fat is needed, the separator is an exemplary piece of equipment. I use one at least once a year, at Thanksgiving. But it cannot produce a perfectly defatted broth, which is generally what you're after. So if your broth is going to involve any but the leanest of flesh or fish, you'll have to defat it by cooling it till the fat has congealed at the top and then scraping away the hwole top layer. My favorite routine for producing a planned broth is: 3 hours in the crockpot, 3 hours on the counter, 3 hours in the refrigerator; defat; voila, broth.