Your beginning house has a flagstone area in the southeast corner for a kitchen to be placed. Since you don't start out with the cooking workshop, you will have to buy it from Ivan when he is in town on the weekend. The Small Kitchen can be purchased for 1000 G on the 1st of the season, and the Knife, Frying Pan, and Mixer can be bought the 19th.
Once you've upgrade your house Ivan will allow you to purchase the remaining kitchen utensils (the Steamer, Pot, and Oven) after you've bought the Large Kitchen. The counter on the left-side of the kitchen is the no-utensil area, and can be used if you own the Small or Large Kitchen.
If you haven't purchased the cooking books from Russell, you can experiment with ingredient combinations and hope the result is not a burnt dish. Since there's no way to know what skill level each dish needs without the cookbooks, you could be cooking up failures using completely valid recipes. This is especially true with the Knife and the Sashimi recipes; without knowing the recipe you can't make the skillfully sliced raw fish dishes.
It's easiest to just buy the cookbooks and have the list of recipes available when you are working with a kitchen utensil. The exact ingredients needed for a complete recipe will be listed in the book (press the left-shoulder button when cooking) and you can not branch off from the documented recipe. For example, it is common in Harvest Moon games to add fruit like Strawberries to the basic Ice Cream recipe to enhance the finished product, but that is not possible in Rune Factory. The Ice Cream recipe can only use an Egg and Milk, and nothing else can be added.
All variations of the same recipe are documented in the cook books. You will see recipes that could be cooked using a Small Egg, the same recipe with a Medium Egg, and so on. Each variation requires the same craft skill and result in the same cooked dish. There isn't any advantage to using a larger size ingredient over a smaller one.
Once you've made your chosen recipe, you can eat it to regain Hit Points/Rune Points, and even gain stat increases and resistance to status effects. To eat your food, hold the item in your hands and press the B Button. You can only be under the influence of one cooked dish at a time and you will see an Apple ( ) underneath your Rune Point bar during that time. Each cooked dish will last a set number of minutes, ranging from 30 up to 4 hours (240 minutes).
Basic cooking ingredients can be purchased from Emmett's tavern.