When making stock, dice vegetables and do 2 parts water to 1 part veggies. Some sites suggest browning in an oven or a pot before adding water. Simmer for about an hour -- too long as flavor will be lost. Strain out big pieces and then strain. Use soon or freeze (ice cube trays work well if reducing stock -- just add water to get back to appropriate intensity.
Other tips:
One recipe suggested adding dried mushrooms and soy sauce for a deeper flavor. Another mentioned that mushrooms are the key here as they add a ton of flavor (surprisingly). Starting with cold water makes sure veggies with different ideal solubility temperatures share all their nutrients and flavors. Taste as the stock simmers, as the flavor will change. Add a bit of salt, but you can always add more to whatever you use the stock to make. And the NYT recommends a pressure cooker.