Madeleine Chu will give you the quest. Once you complete the quest, he will sell you cooking items. Charles Orleans will teach you about cooking. Once you complete the quest, he will lend you cooking manuals.
2. Talk to Madeleine Chu.
Out of the three options it gives you, chose "I want to learn how to be a cook". Madeleine will ask you to speak to her master. In order to show your enthusiasm, you will be asked to wear a cook hat.
3. Wearing the cook hat, talk to Charles. After talking to him, he will chose a random level 1 food to make. He'll tell you the ingredients for this food, and you'll need to bring them to him.
4. After bringing him the required items, you'll make your first food item together. He'll give you the food item that was created, but you may want to hold onto it for later.
5. After you're done making the food, return to Madeleine. Madeleine will let you have his copy of the, and give you 10 .
6. Now that you have a Level 1 Cookbook, you'll be able to make food items on your own now. Madeleine will sell you Outdoor Cooking Sets for 500z, but still won't sell you any Home Cooking Sets.
This time, you will need to ask them if they want to see your cooking. You will be asked to create one of each kind of level 1 food (Look in your cookbook for recipies).
7. Once you're done, bring Madeleine your foods that you've made. You can use the one you created with Charles as one of these foods. Madeleine will package these foods in a "Bundle of Food", and you'll need to bring it to Payon.
8. Deliver the bundle of food to Servant in Payon (208, 127), and select the option "Actually, Madeleine sent me...".
9. Return to the Prontera cooks. Madeleine will give you 10. At this point, Madeleine will allow you to buy Home Cooking Sets for 1000z. They're a bit pricier than regular cooking sets, but the bonus success makes it more useful.
10. Talk to Charles once again. Charles will now let you use his cookbooks if you help him with some items he needs.
The quest is complete at this point. If you want access to higher level sets or cookbooks, you'll have to find them from monsters.