Trim the root end and the top of the leek, leaving some green intact or discarding all of it, depending on the recipe. Discard the outer leaves and split the leek into quarters or halves almost through the root. Rinse the leek under running cold water, flooding it down to the root and shaking to loosen any dirt. Reassemble the layers for cooking. If the leek is to be sliced or chopped, cut it before cleaning, rinse the pieces thoroughly in a bowl of cold water, and then transfer them with your hands to a colander to drain, leaving the grit behind.