They're flavorful! They're free!
As for how I make them: Start with any vegetable (or fruit) scraps and peelings (as in carrots), stalks (as in broccoli and cauliflower), leaves (as in celery), etc. Also use any vegetables that are getting limp or that you know would otherwise go to waste. Put the vegetable pieces in a saucepan, add water to cover 2-3 inches and then simmer on low until the water is half volume. Drain and toss the veggies out (They will be tasteless at this point). Depending on the amount of broth I have after straining, I either put it in freezer-safe cups or ice cube trays. Also, when I use a vegetable or fruit I have canned for meals, I pour the leftover juice/syrup into ice cube trays. When I am blanching veggies for the freezer; I save the veggie water, add in the peelings, scraps or ends and proceed as above. For corn, I take a huge pot and using the cobs after I have cut off the corn for freezing, pack them in tightly and then add water almost to the top, cooking down to half. I save all my fruit syrups over the year, freeze them and use them for desserts and canning.
As for how I use them: For added flavor to everything I make, I use these wherever I would use water. I use them for making rice, couscous and pasta; adding to soups/stews/chilis; adding to meat broths, sauces, gravies, stirfrys. Use them instead of water, in all or part, for poaching liquids and brines. I use these sometimes for just a "hint" of a veggie flavor or when I do not have that vegetable on hand but want it's flavor in a dish. I use peach and/or pear syrup, saved and frozen over the past year, for making applesauce in the Fall. What a delicious difference! Veggie broths and fruit syrups are also great for health drinks, smoothies and cocktails. Use broth instead of water for rehydrating veggies or dry soup mixes. Use your imagination!