Place the head of broccoli on a cutting board. Using a sharp chef's knife, slice through the stalk to separate it from the head about 1 inch below the base of the head.
Trim the stalk to cut off the brown/old end and use a paring knife or vegetable peeler to peel the outer layer of the stalk all the way around. Set aside.
Cut the head of broccoli into florets by slicing through where the stems meet. Continue cutting into smaller pieces as desired for the specific recipe you have in mind.
Florets can be chopped further for chopped salads or broccoli "rice".
The stalk can now be cut into long strips for eating raw or chopped or minced for use in recipes.