Stored loosely wrapped in plastic (to keep them from drying out and to contain their smell) they will keep in the fridge for a week.
Remove any tired or damaged outer leaves. Trim the rootlets at the base and cut off around a half to two thirds of the dark green tops. Partially cut the leeks in half lengthwise, starting at the middle and running the knife up to the green tops. Make a second lengthwise cut perpendicular to the first, allowing you to fan out the leaves. Give them a good rinse to remove the dirt that can get trapped inside as the leek grows. If you’re not cooking the leeks whole then give them another wash after chopping them.
Undercooked leeks are tough and chewy and overcooked leeks can take on an undesirable squidgy texture. Cook until just tender, testing by piercing the base with a knife. Braising in a moderate oven will take anything from 10 to 30 minutes depending on size. They can also be boiled or steamed.