I do very simple approaches. I think dudes do far too much chit chat and waste time. If I approach her and the vibe is good then I'll see if logistics are there to take her on an immediate coffee/drinks date. If the logistics aren't there because I'm with friends, or she's on her way to do something then I'll typically leave her with my card and see if she contacts me later. I find it's way better to leave a girl with a card because then she has to initiate the contact and you're in a way stronger position.
My dialogue is I'll go up to a girl and say "Excuse me" and then I'll make some kind of comment about her fashion, what she might be doing, or her mood. I never compliment her beauty or anything like that. I never ask her any questions either, I just make comments. I'll keep making comments about her until she offers me something back, for example I might say something like "You look like you're on your way to a party", and she might offer some information like "Actually, I'm on my way to a dance class" - then you start making comments about dance such as "You look like you're a jazz dancer, I can imagine you dancing to a saxophone song" (on and on it goes until she is hooked and smiling etc). After I've done that for no more than 5 minutes I'll close her by saying "Hey look, you seem quite interesting. I'm just with my friend at the moment, but I'd love to catch up with you soon and get some (insert whatever you like here - tea, drinks, coffee, noodles)." - then i'll hand her my card and tell her to text me.
If the vibe is good and I have some free time, and she appears to be free too then it's pretty much the same close "hey you seem quite cool. I'm on my way to a coffee shop, come with me. What kind of coffee do you like?" - that's an insta-date if she agrees and it's always the best outcome if you can get that. Take her on a good insta-date and you can either bounce her home that day, or bang her on the next date.
The most important thing with Daygame is you DGAF. You'll get outright rejected sometimes. All good. The rewards are worth it but you have to remove all ego.