Cooking in London Life will allow you to create your own food, which makes it easy (and cheaper) to boost your Happiness.
Buy a Table
In order to cook, you need to have a table in your room. Tables can be purchased from all sorts of shops in Little London. Chess Department Store has cheap tables. Put the table in your room.
You can learn recipes simply by eating food. However, you won't be able to learn complicated recipes right away. Simpler foods are easier to learn the recipes of. Try drinking coffee in a café to learn the coffee recipe.
How to Cook
To cook, all you need to do is return to your room, examine the table, then choose a recipe that you know. You won't be able to cook until you know at least one recipe.
After you choose a recipe, you will attempt to cook the item. If you don't succeed, your Happiness will decrease. Therefore, to minimize a decrease in Happiness from a cooking failure, you should wear an outfit with high Coolness while you cook.