Leeks are a notoriously dirty vegetable, and it’s because of how they’re grown (in lots of dirt). Most farmers push dirt up and around them as they grow, which keeps the stalk pale and tender (the dark, green parts are much tougher than the white and light green parts). This, of course, results in dirt and sand getting all up inside the many layers of the allium. It’s not that big of a deal; you just have to clean them before you eat them.
I prefer a whole-leek cleaning method, such as the one use by David Lebovitz. Keeping the leek whole while you wash it makes it easier to manage. Instead of a bunch of little leek slices floating around in a bowl, you only have to keep track of one, large, fanned out vegetable. Like Lebovitz, I start by trimming off the truly tough, dark green parts of the vegetable (to save for stock or steaming), as well as the whiskery root end. (Don’t lop off the entire root however — that’s what holds this whole operation together.)
After you’ve trimmed both ends, make one large slice through the entire leek — starting from about half an inch from the root — all the way to the end. Rotate 90 degrees and repeat.
Once your leek is all fanned out and floppy, swirl it around in a plugged up sink or very large bowl of water. Agitate it a little, then give the inner layers a visual inspection to make sure you got all the dirt out. If it’s still dirty, change out the water and try it again. (Some leeks are dirtier than others.)
Once your leeks are clean, set them on a kitchen towel or in a dish drying rack to dry. You can leave them whole (a good move if you want to grill them on hot coals), or slice them into smaller pieces for soups, stews, and sauces.