It’s not rocket science! You go about your lawful occasions. You come to a stopping place -bus stop, waiting for the lift (elevator) to arrive -and someone else is there. If they are on the phone, or using any other device, you ignore them as they ignore you. If they are not, you nod and smile politely. If they don’t respond or they look away, you leave it at that. If they return your gesture, you make some comment on the weather, complain about it being Monday, or rejoice about it being Friday. The nature of their response will clue you in as to whether they are willing to engage with you, and at what level. It’s no different for women or men, though it has been my experience that women in general are more likely to respond than men. Of course, some may actively attempt to engage you first, in which case your response is up to you.
This is called being an adult. Why do some people find it so hard?