Court-bouillon
This is the simple method consisting of simmering crustacean shells or fish trimmings in water. 

Depending on your preference or the recipe, you can add some saffron, white wine or tomatoes.

Fish stock
This is a more concentrated court-bouillon and generally more elaborate in its ingredients. 

For the cooking time, you simply have to reduce the broth by half. 

Fish soup
Simply prepare a fish stock; a few minutes before serving, poach your fish in the stock. 

You can add some julienned leeks, serve it Provençal-style with rouille (saffron mayonnaise) and croutons, or top it with a spoonful of lemon whipped cream topped with some northern shrimp. 

Sauce
If you let the stock reduce even longer (to a third) you can whisk in some pieces of butter and a little cream to make an excellent sauce. 

Tips
Because of the reduction, taste and add salt as needed only at the end.

If you have mollusks on the menu, open them in some fish stock to begin; remove the meat and return the empty shells to the stock to flavor it; remove them at the end of the cooking time. 

1. sweat the onions, celery, thyme, parsley and bay leaf in a pot: that is, heat them over low heat in a little butter for 3 minutes or until the onion is translucent; 
2. add the fish carcasses, lemon and pepper; cook gently 3 minutes longer; 
3. add the water (and wine and tomatoes, if using) and bring to a boil; 
4. skim the surface; reduce the heat and simmer for an hour for court-bouillon and 2-3 hours for a stock;
5. if you're using saffron, add it an hour before the end of the cooking time;
6. strain and use according to the recipe.