What do you do when you see a woman in tears?

I would walk very far away and let someone else handle that. I'm aware of my ability to help, and this is not within my set of skills.

Give a bear hug

Really depends on the girl and what I know about them. If it's a stranger I'd probably just ask what's wrong, like any other person. Peeps I know personally gets hugs if we're on friendly terms ^.^

In the city, on the street, I leave people alone who are crying unless they look like they actively need help.

I'll say "sorry, pardon me, how can I help you?"
and place a hand on the persons shoulder

It depends. Some women cry over nothing and I don’t pay them any mind.

I would directly approach her and ask her if she was ok, etc. (i.e., first ascertaining whether or not she was injured physically, in distress because someone *else* was injured, physically, then move on to figuring out what was going on beyond a physical injury and comforting her as needed).

Offer her tissues, and a comforting hug, and ask if there’s anything I can do to help

Feel sad.😭