Grab the thick stems and pull the bunch of leaves off. Discard the stems and chop the leaves, including the smaller stems that the leaves are attached to. Just chop them fine and the small stems will blend. My wife pulls the leaves off individually, which takes forever, because she thinks the stems are undesirable, but she doesn't even notice when I just chop them up together.
BTW, cilantro is completely unrelated to tarragon, as another poster has suggested. Cilantro is the coriander plant, and the dried spice that is called coriander comes from the roots of the plant.
Black bean salsa good.