Ah, well I can often be very awkward, and the harder I crush the worse it is sometimes.

But I just start up a conversation. I think what has given me some level of success as opposed to guys who are just looking to "pick someone up" is that I only do it with women I am genuinely interested in. So, sort of by default that makes me a better listener and so on.
I also acknowledge that I am just a more shy person. So I accept it, and if worse comes to worse, I just laugh at myself (and try not to be self-deprecating, though that sometimes fails) and it often puts the girl I am talking to a bit more at ease with it too.
Also, even though guys are generally expected to be the one to initiate...women are often scared and have their hangups too even if they are the one approached. Wondering if you're really into her or just want to get in her pants. If you would think she was ugly without makeup or whatever. Some women have been asked out just as a joke or to prove a point. Or she may wonder if you're just a creeper who might not treat her right. So the best thing, to me, has always been to just be genuine, not put all the pressure on, and see it as a chance to get to know someone who could be a part of your life. Women and men aren't all that different, really, it's just another human being trying to find their way just like you.