In order to gain a cooking skill you must first finish the cooking tutorial successfully. You must keep the pots cooking without allowing them to boil over. To do this, touch a pot to select it then shake the iPhone to keep the heat down and stir the pot. Do this enough times in the allotted amount of time and you will earn one point.
In order to cook in general, you must first purchase a recipe from the local "Corsican Bistro" located by the beach. Once you have done this, go to the grocery store "Quickmart" to purchase your ingredients. You can also grow them in your garden if you have already upgraded your house, which saves time and money.