Flaky pastry is made by "cutting in the fat" (shortening or butter), also known as "cutting in". It means to combine the flour with the fat in the recipe as quickly as possible. The fat must always be evenly sized, coated with flour and distributed throughout. When these fat pieces melt into pools, they give layers for flakiness. 

For making pie crusts, cut in the fat until all of it is roughly the size of small peas and the texture of bread crumbs. If it is cut into smaller crumb-sized particles, the pastry will be less flaky but more tender and mealy. On the other hand, for biscuits, the fat should be crumb-size.

"Cut in the fat" is accomplished with a pastry blender, two knives or your fingertips. Don't press down on the fat and flour while cutting it in. It needs to be incorporated into the flour as quickly as possible without overhandling the fat so it softens or melts. If it does, you won't get flaky pastry. If the fat becomes oily because the rubbing-in takes longer and everything is too warm, refrigerate or freeze the entire mixture as is until chilled and then try again.

Start with chilled or frozen butter (frozen is better). Measure and cut the butter into small, evenly-sized 1/4-inch cubes. This makes it a perfect size when later blending it into the flour and dry ingredients. I then return the fat to the freezer to chill again. Toss the chilled butter cubes in the flour mixture. 

Then, cut the butter in. As you do, occasionally lift the butter and flour up high with your fingertips and let it fall back down into the bowl, which means that air is being incorporated all the time, and air is what makes pastry light.