The best way to get a girl's phone number is NOT to ask but to TELL HER to give you her phone number. And the best way to ask a girl out on a date is to SUGGEST A DATE with place and time. Here is an example of how this might work:

You (getting her number): "Let me grab your number before I head off" or "I should be getting back to my buddies but give me your number - I've love to take you out for coffee sometime".

Begin a conversation by text using an opener that isn't boring. Possible topics can be based on common interests and should flow naturally (i.e. don't make it like a job interview). Arrange a date when you're ready and context is appropriate (but don't wait too long!). Suggesting a date might go something like this:

You (arranging a date): "Hey [her name]. I remember you telling me you love painting almost as much as I do. It's paint-a-flower-pot night at [name of venue] this Saturday. How about I pick you up at 7."

If she says she's busy, suggest that she choose a time/date and follow up a few days later. Don't blow up her phone with texts.

Bonus tip: Get her contact info in the middle of the initial conversation at a high point, not at the end when the conversation has gone stale. She will be more inclined to give it to you and you'll have something to talk about when you text or meet again later.

Edit: Your/her mix-up fixed.