There are three basic methods for mixing most cookie doughs, and all three methods produce essentially the same results.
The food processor is my first choice because it is the fastest, and it also makes it possible to use fine granulated sugar in place of superfine (because it will be processed into superfine during mixing). This method is given where applicable. If you are making a small batch of dough and your food processor is too large, you will need to scrape the sides of the bowl often or use an immersion blender.