I've never really understood people who say they can't cook. After all, as long as you understand how to follow directions in a recipe, you can cook. Once you know the basic techniques, you can read a recipe to make sure you have all the ingredients and equipment and off you go.
Recently I was on a phone interview with Clotilde of Chocolate and Zucchini, and she mentioned the importance of being able to cook without a recipe. This requires some confidence and some capability. You have a better chance of successful improvisation and creativity if you have a very firm grasp of the basics. Creativity can be inspired in many ways, a meal in a restaurant, a new cookbook, a trip to the market, etc. But improvisation is a different matter.
Improvisation is "a performance given without planning or preparation". So basically you are relying on your brain for inspiration. Sally Schneider's new book, The Improvisational Cook is an exploration into the concept of improvisation in the kitchen and provides some wonderful recipes and ideas along the way. Schneider explains how recipes work in a section called "Understanding", and then various riffs on a single recipe.
How does it work? Here is an example of an idea and recipe--the author begins with a Lemon Oregano Jam that she first tasted at Mario Batali's restaurant Babbo. She explains that the technique of pureeing the whole lemon is crucial and that the addition of oil helps to round out the flavor and creates an emulsion. In addition to the original recipe, her variations include Lemon Lavender Jam, Tangelo Jam, Tangerinesicle Parfaits, and Meyer Lemon Dessert Sauce and Filling.
Just as in jazz, the best improvisations come from the best musicians and Schneider is an accomplished cook who you can trust and will in all likelihood inspire you as well.