Mix lightly for flaky pastry
Most pie doughs are basically made of flour, fat, and water. The fat is cut into the flour to form crumbs, varying from a meal-like consistency to pea-size pieces. When these crumbs are moistened with liquid, they form a malleable dough. When heated, the pieces of fat melt, and the liquid in the dough steams apart the pockets left by the melted fat. As the dough bakes, the moisture evaporates, and the dough dries in layered flakes to form a crust.
Begin with cold ingredients. Keep your measured and diced butter and shortening well chilled until ready to use, and use ice water for the liquid. If the fats melt before they're in the oven, they are absorbed into the flour, and any chance of producing a flaky pie crust is lost.
A food processor works great—to a point. Many bakers only make pie crust by hand, swearing that this is the only way to control the dough. Others use the food processor exclusively, exulting in the ease and convenience. I use a processor for the first step—cutting the fats into the flour, which works really well (see my Flaky Pie Pastry recipe for details). The trick is to keep an eye on the consistency of the fat and flour.
When it comes to adding the liquid, however, the food processor has a few drawbacks. If you add the liquid with the processor running, it's difficult to distribute evenly—something that's crucial to a tender pastry—and the dough can form a wet mass around the steel blade before a sufficient amount of liquid has been added. To avoid these pitfalls, I dump the flour-fat mixture into a large bowl and add the liquid by hand.