I'm not an authority by any means, but when I was just a lurker here years ago one of the earliest and most useful tips that I took away was this.....Someone posted that there is exactly one way to ask a woman for her number: "What's your number?"
Brutally simple, removes extraneous straws she can grasp on to shoot you down with, and demonstrates you have the balls to cut to the chase and act decisively. Unlike so many otgrr areas of game, especially when learning, it's beautifully simple, really.
You still have to warm up to it in conversation, but once you know when you are good to ask for a number, it's pure gold. Has never failed me once. Sure, you're still going to get shot down sometimes, but it's the kind of shoot down that let's you smile and walk away with your head high and your balls intact instead of getting shot down with her saying "i don't like fish" because you stood there and meandered into asking for her number with some run-on-beat-around-the-bush excuse of a number close like "You seem really nice and I'd love to show you my saltwater fish tank so can I have your number?" that you squeeked out like a snivelling weenie. She may or may not shoot you down, but make her shout you down like a man, not because you gave her 7 ways to gracefully do it by not being able to do something so simple as to ask for her number and she smelled the desperation on you. "What's your number?" is so simple and easy it just smooths right past all of that without you getting a chance to get all self concious about it.
When I was last here about a year ago guys were even talking about handing her their phones and just saying "give me your number" so it isn't even a question, at all. Personally, I would save that for when you get a bit more advanced. "What's your number?" is pure gold, IMO.
Good luck.