When the bag was full (after 3-4 weeks), I filled up a giant pot of water, added the veggie bits, and set it to cook. I also added a few herbs/spices to the mix: about a teaspoon of peppercorns, some thyme, and a clove of garlic. Oh, and about a teaspoon of salt (but you can totally do more than that.)
I let it simmer for a couple of hours and basically ignored it. It came close to boiling over once, but I just turned it down. The above picture was taken towards the beginning of the cooking process; by the end, everything was pretty much brown and mushy- all good!
Then comes the storage part. I didn't want to go through the trouble of canning it (which I'm sure you could do), so I just ladled it into pint-sized jars, and let it cool on the counter. I used tongs to take out the big pieces of vegetables, and put them into a large colander that was over a plate (to catch any extra broth that came off of the veggies.) I used a canning funnel to make sure that the broth went into the jars instead of all over my counter, then I popped some tops on them, and froze them after they were at room temperature. That's it! I needed a fine strainer when I got to the bottom of the pot, but it was really easy. You should totally do this, especially if you make as many soups as I do!