You can often tell girls who have boyfriends from those that are single. It's not 100% fool-proof but what I've found is that girls who are single/looking typically put more time into getting prettied up when they go out for mundane activities. (i.e. they want to be noticed) Women who are in secure relationships usually don't put quite as much time into it.
That's just a rule-of-thumb and often, women deviate from it. Best way to find out is to talk to them. Don't ask, though...wait and see if she brings up her boyfriend. If not, proceed as planned.
You MUST be completely secure and comfortable with talking to a "strange woman", though. Take charge of the conversation.
Think of the times you've been in a strange place with strange people and someone struck up a conversation with you and you ended up liking that person. They have a way of acting like "talking to strangers" is the most natural thing in the world, don't they?
Girls are wary of "strange guys", even if they're cute. They will try to roll you back on your heels by making certain comments that seem on the surface like "signs of non-attraction". You have to laugh them off. Don't even let them phase you. Watch her body language, they way she uses eye contact, aligns herself to you. Pay attention to the emotions she displays when talking to you, the pacing of her conversation...when she hesitates, when she giggles, when she seems shy or hesitant, when she seems open.
The words are interchangeable. The problem with "day-game" is that most men fail to read body-language, instead focusing on the words, trying to play "20 questions" to try to "get to know" a girl. What you say is just to keep her mind distracted while you try to establish a "rhythm" with this girl. What you're looking to do is to have her feeling a kind of "hasty friendship" with a little bit of sexual tension by the time you get the number.
Think about how you interact with your friends or lovers. After like, date 2 or 3, you're not asking them stupid "getting to know you" questions any more. You're not trying to get them to talk about themselves...all that crap's been done to death and you're just making observations and playing off of one another's thoughts and feelings.
What you're working for in "day game" is just that...reaching a state of rapport where she thinks of you and her as an "us" rather than you as you and her as her. This is hard to do for someone who's socially inexperienced, because it requires you to learn a lot about someone very quickly, what they think, how they think, what they might find interesting, what makes them laugh, what "excites" them.
That's what you should be working on when you're running 'day-game'. Practice observing a girl's state of mind and setting up a "hasty friendship". Try to establish rapport with strangers instantly.
Once you get good at that, you can try injecting sexuality into it...and that's done by adding elements of eye-contact, kino, etc...just Gunwitch it. Let yourself get a little horny while setting up this "hasty friendship" and it permeates the dynamic and becomes a prelude to romance.
This is the same kind of crap that's done in bars and nightclubs, but there, you can afford to be significantly bolder with the physical/sexual overtones.
And like in bars and nightlcubs, it helps to look your best. Just because it's "day-game", it doesn't give you an excuse to be lazy.