Because it's cooked for a half an hour at most, a court bouillon never reaches the same level of flavor or complexity as a full-term stock. This sounds like a negative, but a court bouillon is actually useful for cooking mild-flavored things like fish or vegetables. In these cases, a full stock would tend to overshadow the natural flavors of the food, but a court bouillon gives just right balance of flavor and delicacy.
Traditionally, court bouillons are a simple combination of water, bouquet garni, and an acid - no bones or other animal parts. This acid can be white wine, vinegar, or even lemon. A mirepoix of carrots, celery, and onions or leeks can also be added for extra flavor. Everything is simmered for about a half an hour before the liquid is used for cooking.
In general, a court bouillon is not meant to be eaten itself or reused many times.
Here are a few recipes from around the web!
Related: Tip: Save Vegetable Scraps for Stock