To make the stock, simply add the trimmings to a large pot with olive oil, salt and some fresh or frozen thyme over medium high heat. I like to use Crate&Barrel's Utensil Pot Clip (pictured) when doing this, since lots of stirring is involved. Once the trimmings have reduced (about 20 minutes), I add enough water to cover the vegetables, bring to a boil, reduce the heat and simmer for about an hour, stirring occasionally.
Once the broth is cool enough, you can strain the vegetables through cheesecloth to squeeze out all of the flavor. You can also use a potato masher if you don't have cheesecloth handy—just be sure to strain the final product again through a fine mesh strainer. I store the broth in 4-cup plastic containers for easy use—it will last 2-3 days in the refrigerator or up to 3 months in the freezer.
Here are some of the trimmings I use to make the broth:
brussel sprout ends
celery ends/leftover pieces
kale and/or collard green ribs
onion ends (use the papery skins as well)