Here you will learn what Dishes are and how to Cook them in Lost Ark. You will find out how to source ingredients and what you need to do to get a dish added to the Adventurer' Tome.
The name Cooking is a bit misleading. You don't really cook yourself; instead, you will provide the appropriate ingredients to in-game cooks, so that they can prepare dishes for you - eating them counts towards your progress in Adventurer's Tome, and therefore towards the game's overall progress. It also gives you the chance to earn interesting rewards. Completing these tasks is easier than, say, finding numerous secrets. An example of such an NPC who will ask you to find dish ingredients is Hely, the Cook (cook hat icon on the map) in Prideholme.
By interacting with her, you will see a list of recipes. On the right you can see the ingredients you need to collect/find, and the price for making the dish. You only need to make one dish and eat it when it is in your inventory to gain progress.
When you move your mouse over an ingredient, you'll see where to look for it. Sometimes they are linked to quests, rapport, etc. If you need to find it through exploration, go to the designated area and look for interactive objects. It is not easy, and sometimes the hints are quite obscure.
Some recipes are not associated with cooks. For example, you can buy one of the dishes in Prideholme from Veda, who is an ordinary potion merchant.