1. Keep a handkerchief on your person. A clean one, since it's not for you. It's for the crying woman.
2. When you encounter the crying woman (and she needs to be sobbing as if she's been hurt — never approach a woman who is merely weeping or teary), approach her as if you're advancing on a wounded animal that might still be able to bite — slowly, thoughtfully. Pull out the handkerchief.
3. Say: "I'm sorry to disturb you, but is there anything I can do to help?"
4. Whether she responds or not, offer the still-folded handkerchief. Point out that it's clean. This should make her laugh.
5. If she hasn't yet told you to go away (and if she tells you to go away, do so immediately), ask what you might specifically be able to do: stay with her, call the police, listen to her problems, tap dance.
6. Proceed according to her wishes until she says she's fine. Tell her to keep the hanky.