Join the crowd – leeks are notoriously difficult to clean. The best method is to trim the tops of the leeks, discard the outer leaves, and trim the root. Split the leek in quarters almost entirely through the root. Rinse it down to the root in cold water, shaking it to loosen all the dirt. Finally, reassemble the layers for cooking.
Of course, if the leek is going to be chopped or sliced, it can be fully quartered or halved before cleaning.