More cooks could become better soup makers if they just set aside their cookbooks once in a while and think about the cycle of soup.
First, you make a broth or stock. Take those trimmings that you would have thrown out, skin and tendons of meat, or the carrots, celery, tomatoes and onions slightly past their prime, and cover them with water and a little salt, add a bay leaf and a few peppercorns, and simmer for several hours. Strain and then you can toss the cooked remains into the garbage or compost. For meat liquids, put in the fridge or freezer until the fat congeals at the top, then throw that out, too.
If you're not ready to use it, put it in a container marked with the date and contents.
When you're ready, you can get creative. Use leftovers in your fridge if you can. If your broth is strong enough, a little vinegar on a cup or less of leftover pasta salad will be absorbed and add to the flavor of your soup. Or maybe you have a cup of leftover rice; add it to 2 cups of chicken broth, bring to a boil with the rice, then stir a little of it into a cup containing a beaten egg and the juice of a lemon. Turn the soup down to a simmer. Gentle stir the contents of the cup into the hot soup.
Experiment. If you like a combination of spices in a dish, chances are you will like it in a soup with similar ingredients. Just be aware that as a soup cooks, water evaporates, so the spices will intensify, and not all at the same rate. Chilies can be a lot hotter in soups, as can pepper. Basil may disappear (that's why it's good to add fresh basil just before serving). Lemon can brighten a bean soup; sherry can make it richer.
If you're lucky and you like soup, you may never have to throw out any leftovers again.