Most soups have two or three ingredients with no duplicates.

Whenever you try to cook a soup, if you put in the right combination into the soup bowl, the name will change to reflect the recipe you've made, and you'll unlock the recipe.

However, if you put in the wrong combination, and cook it anyways, you can still discover recipes. If your recipe is only 1 ingredient wrong, you'll discover the soup recipe whenever the soup finishes cooking. For 2 part soups, you only need 1 ingredient right, and for 3 part soups, you only need 2 ingredients right. You can only discover recipes that have the same number of ingredients that you put in.

There are some 1 ingredient soups, these you can only get by putting solely that ingredient into the pot.

Other than that, it's down to luck and educated guessing. If you want a tip to get you started, here's a tip: A good, sustainable early game soup can be made exclusively with drops from the Pest and Peccary.