When you approach a girl, you have to ask for her name, it's a must. And do so as soon as you can. Give her an identity, she isn't just the girl I seem to be interested, she's a human being with a life story and a soul, call her by her name, when you think of her, use her name, she'll seem more important, plus you will show her that you care who she is.
You always meet someone within an circumstance, it's obvious, I know, so take advantage of it. I meet a girl at a video game store once that caught my attention a lot, I asked her if she liked video games and thus we started a conversation that lead to other topics, finally, when I paid what I had bought, I asked for her name and she very kindly gave it to me with a smile, it isn't that hard, but you got to be confident.
Take advantages of the circumstances, I think church is quite an easy place to approach a girl. Cause you're not starting from zero, you know there should be some kind of spiritual link between the two. Asked her how long she's been there, what she likes the most, ask about her family, just ask, be creative, but always start with the basic, introduce yourself and ask her name, hope it helps!!