Step 1: Chop off most of the green end, leaving about 3 inches of green still attached. You can rinse the green you chopped off, and use it for a stock or a broth, or you can discard it.
Step 2: Slice length wise, down to about an inch from the root. Do not remove the root yet, it helps keep things together, while chopping.
Step 3: Rotate and slice again, dividing the leek into quarters, like this.
Step 4: Rinse, pulling back sections and getting out any trapped dirt.
Step 5: Slice as thinly as preferred for the recipe, up to about 1/2 inch from the root. Discard the root.