Slice off the root end of the stalk. Peel off one or two of the tough outer layers.
If you want to release more of the aroma and flavor from the lemongrass (for instance, if you are using it in a marinade or a cocktail), you can pound the bottom half of the stalk with a rolling pin or a meat mallet.
Slice across the bottom of the stalk until you get to the skinnier, less tender upper part (see Note).
Continue chopping and mincing the inner lower part of the stalk until it is as finely minced as you want it for your recipe.
Video
Notes
Reserve the top outer layers of the lemongrass for another purpose, like a simple syrup or tea. This can also be pounded to release more flavor, but it will not be tender enough to eat.