I've always gone the light-hearted casual route. Just throw something out there and see what the response is. If you're already good friends, perhaps a simple joke about dating or "hooking up" would be taken well. If she says yeah right, then you've not really committed yourself. And, if she flirts back, and ups the ante, then you've broken the ice.
Many of my girlfriends became girlfriends after simply doing some rather innocent flirting and then peaking their interest to the point that they just had to go for it.
And, depending on the girl, sometimes a direct "hey, wanna f*ck" is all you need. Either they blow it off as a light-hearted joke, and you have some fun with an interesting conversation, or you find that they're interested and get together.
But, then again, I used to make a lot of suggestive comments (which were really just in fun) to most of my female friends. And, we were all used to flirting for the hell of it and just having fun. So, I could just throw something out there and see which way it went. Either way, it was always fun. Either it led to a very interesting and fun conversation, or it led to something... Shall we say hotter. Sometimes I got both reactions (which was particularly nice).
Be careful though... Last time I made a suggestive comment to a woman about just having some fun, I ended up married (been nearly 15 years now).
But, that's not bad either. Now I can just say what's on my mind, and tell her as directly as I want. Sure, there's a time for soft and gentle approaches. But, the more direct ones will usually get you a response other than being softly declined.
I'd rather put it directly and either have a fun flirtatious conversation (or be taken up on my offer), than take a soft gentle approach that would be easier to decline.
Think of it this way... You go up and say "would you like to go out with me?", and she says (likely in a very gentle and polite way) no thank you. Or, you can just be direct, and then most likely even a rejection would be fun and take the relationship to a more interesting level.
If you up the friendship to fun and flirtatious, then at least you've gained some ground. Then, perhaps you'll have some more interesting and flirtatious conversations. And, perhaps over time, she'll decide that she'd like to do more than just talk about getting together.
Of course, I guess that all depends on the girl. I've never really gone after the shy quiet ones. So, if the innocent type is what you're after, then you're on your own
