Genuine compliments work great.
-I just want to appreciate...(fill in the blank, based on an actual observation about her.)
I just want to appreciate how relaxed you are right now
I just want to appreciate this sweater you have on. It is very creative
I just want to appreciate that you can drink a coffee that large and still be so chill
I just want to appreciate how vibrant you are this morning. Definitely have the biggest smile in here
-Congratulations on... (fill in the blank, based on an actual observation about her.)
Congratulations on having the most colorful shirt in the whole shop
Congratulations on having great taste in pastries
Congratulations on studying harder than anyone else in here right now
Situational openers also work great.
These are generally very indirect and require a smooth angle of approach, so as to make it feel natural and not forced.
-(looking at the artwork she is sitting next to) How much coffee do you think it takes to paint something like that?
-(A shady corner of the patio under a big tree) Well this is definitely an inspiring little nook. I bet you're getting your best work done under the tutelage of this epic tree
-(She is sitting near the take a book leave a book shelve) Great place to sit, when you are done with work you can grab a life-changing book.
Keeping it simple can work great (in the right circumstances)
-(Passing by her table and she makes eye contact with you) "What do you think would happen if we took a moment to meet each other?"
-(Sitting at the table next to her) "How's life in this corner of the world?"
When she is just on her laptop and you can't find ways to implement the previous openers
The angle of approach and your presence is pretty key here. You don't want to want to just b line it straight at her. Make feel like you are just passing by casually and happened to see her just in that very moment
-"Solving the world's problems over here?"
-"How's the novel coming?"
-"May that be the last email you have to send today"
-"Does your boss know you're just at the coffee shop watching youtube?"
A couple of notes here. First, you don't actually want to be snooping on her screen, so approach at an angle where it is clear you are not doing that. Second, this can be a bit tricky to transition out of as she is probably a bit engulfed in whatever work she is doing and someone commenting on the fact she is staring at a screen can be a bit of an interruption. You will be able to pick up pretty quickly if she is totally not open to conversation. If she seems a bit open you will have to stick the landing so be prepared to think on your toes and come up with a good follow-up, to really get the conversation going. After this kind of opener, she will often correct the assumption you made "Oh no, no emails, just working on my website" but obviously her responses can carry depending on a lot of factors.
Pre-gaming the room
While sometimes you might meet a woman in a more spontaneous manner, a huge part of coffee shop game is about how you pre-game the room. Enter the room with the presence and casually stroll throughout the space in a manner that really conveys you are at home and at ease. Take your time to assess the space, and where you want to position yourself. When you enter the space in this manner you will stand out a bit and you will surely catch the attention of some people, eligible women included. When you are sitting at your table, be present in a way where you are just taking in the ambiance. If you have a book or are working on something, take long thoughtful pauses and just be present in the room. Not only does this allow you to better be aware of the women around you and potential moves you can make, but it also gives you a presence that is attractive and intriguing. Long-distance eye contact is a powerful tool as well. When you lay a lot of the groundwork in this way, the approach and opener are just a natural step away from something that has already been set in motion, and not so much of a leap from 0 to 1.