My game is not perfect I have my own sticking points but number closing is not one of them.
Here's how I do it:

Approach:
open the set, I personally use an observational opener if I can but on the odd occasion I'll use an opinion opener especially if I need to open a set quickly and off the cuff.
I've opened plenty of sets with a simple "hi I've not seen you here before".
Your opener is not important it's the way you say it and you need a smile.
If it's a group you will need to engage them all at least once, it's polite and they might be able to introduce you to other girls later in the night you gotta keep the big picture in mind, you also don't want the friends to cock block you.
People cock block because their bored or jealous, you can patch the boredom by bringing them into your conversation and asking their opinion, but be careful they don't run away with the frame because before you know it you'll be talking about tampons and those squishy little pads girls put in their high heels.
A time restrain is a good idea too It will put a girl at ease, Im normally bouncing between several bars anyway so I'll use that or if I'm opening sets by myself I just say "I've got to get back to my friends in a minute"


Mid game
You need to connect with the girl as quickly as possible, being able to open the set confidently and hold a conversation without being weird will go a long way.
I will normally ask her either:
- "when you was little what did you want to grow up to be?"
- "what do you do for work now, (if it's retail or something I'll say "that must be soul destroying I bet your passion lies else where" )
Basically you want to avoid actually talking about their job because any AFC can do that, you can use it as conversational transition to find out what actually makes her tick though. You can use her job to neg her too, especially if she's a lawyer or in a profession that people hate.
After finding out what makes her tick relate yourself to the subject or activity.
I was chatting to a girl on Saturday, I found out she was a manager in retail but her passion was fine art.
I studied fine art for a while so I had an instant rapor builder, I through in that Id been to the guganhein (I'm pretty sure that's spelt wrong) in new york and started to build attraction.
My point is: find what makes the girl tick.
By the end of the conversation I'd built so much attraction and comfort, we we're talking about getting her clit pierced and if the sex would be better.
Number close:
There are two kinds of number closes as far as I can see, a soft number close and a hard number close.
If you haven't built enough comfort or attraction you might still get a number close (soft) but it'll be contrived and you'll see the resistance in her face (you've got a 90% chance of a flake under these circumstances) this is where calibration is paramount, if you are not calibrated and you force an unnatural number close she will most probably flake.
You need to feel when the opportunity is right and properly calibrated(results in a hard number close) otherwise the number is useless, sure you might get it and your mates will think your a legend but you wont get a second date.
If you feel your calibration is off work on gaining more comfort, play a game or sit next to her and people watch, all girls like people watching and negging other girls style.
You can then say "I've gotta go but we should do this again, I know this great coffee place/bar, you get some real freaks in there too. Give me your number."

Or simply "I've gotta go we should go for a drink, what's your number?"

Or the one I used on Saturday: "I would love to make your love life that little bit more complicated, what's your number".

I hope some of this will help you guys.
Voltaire.