With leeks it's very important to get them cleaned well, since there are so many nooks and crannies for grit and dirt to hide in. We're using mostly only the white part of the leek and just about two inches of the green part just above there.
Split the leek down the entire length ...
... and fan it out to expose the grit.
I fill my clean sink with a basin of cool water and swish them around under the water a few times, which seems to work.
Remove, check, swish again if needed, check again and set aside to drain. These need to go through again a few more times before slicing.
Once well cleaned and drained, chop or slice the leeks as called for in the recipe.