Great question not often enough asked. This is the road to riches. I'm still debugging (sorry, geek-lingo) this one.
I never stare at her. I look at her first. If she glances at me and goes back to what she was doing I change position.
I then make sure she sees me looking at her. When I moved, I am kind of turned a bit away, not directly facing her. I look at her sort of over my shoulder.
If she doesn't look back at me in 10 sec, then I'm gone. I could learn more about body language at this stage. If she's really nervous, it seems that I need to back off a bit.
What I wait for is her to look up again, and then I smile at her and give that glint in the eye. Causing your eyes to glint takes practice. Try doing it in the mirror. Women respond to eyes.
If she smiles back, I'll move towards her. If she doesn't move, I speak to her about something really informational like 'do you know where the sex books are?' Ok, maybe not that, but I try to ask a really stupid question that gets them laughing. Sometimes I back off and sort of move away briefly at that stage.
I see if she is looking for me. That's interest level, big time. I move back around and say the same dumb thing I said before. This sounds totally stupid but it has worked.
If I feel that she is really interested, not just amused I'll turn up the heat on her. I'll make fun of her shoes. Boy those are the biggest feet I've ever seen! While pointing to a book on pengiuns.
Stupid and silly I know.
Then I ask if she likes to work out, likes art, likes gardens, WHATEVER. I have places I know to go ready. Most cities have a botanical garden. They are often free and there is no money involved. Of course I have my cell phone and get her number.
I DO make plans to meet her right then. Once a time and place is settled, then I depart. Sometimes she just says no, I'm kind of busy, sorry. I say, OK, nice meeting you.
Success rate, maybe 10%.