At First when cooking is avalable it will be located in the Kitchen in the Three Sister's Inn. When finding the Kitchen you will find there is only 3 Cooking Utensils, which is the Kitchen, the Frying Pan, and the Pot. With going to the Utensils, Odette will come up and ask if "you want to learn to cook?" "Aden" will say yes and then Odette will give you the first Recipe book which will give "Aden" recipes for the Kitchen, the Frying Pan, and the Pot.
To get other kitchen utensils first you need to upgrade your house, to upgrade your house it must be on a thursday at Midday, Talk to James in the Church Plaza to see a list of upgrades for your house and appliances, Select Others and choose to upgrade your house. By doing so an option to add a kitchen will be provided, after adding a kitchen you must buy the utensils such as the Steamer, Oven, and Mixer individually. You can just buy the master level of each and not have to spend money on the basic or advanced levels if you have enough money to do so. Remember that James also has a monthly sale on the 23rd of every month.
Every dish you make has a certain skill level you need to be to make it. If "Aden's" cooking skill is 1 and the skill of the dish you want to make is 5 it will be "somewhat difficult", meaning you will have a harder time making it than the if it was skill 1. If the dish was skill 22 on the other hand you could not make it at all.
*Tip - you can make tons of money by buying milk from the bar and cooking it to make Hot Milk, with some haggling skills a profit of ~100G is attainable, when low on RP either buy some pickled eggplants/turnips or eat some fish dishes you made or go to the Bath House or if Lily is working in the inn you can buy ice cream from her. You can do this trick when on the day that the inn is having a sale to increase your profits.