You need a heavy dose of game my man.
Be confident, be a bit of jerk, and don't self-deprecate. Hitting the weights will help as well if you aren't doing that already.
I still fail to see why people think that works a majority of the time.
Perhaps I'm not articulating it right. I don't mean that Carl should walk up to her and go "Sup bitch!", but my experience is that some gentle teasing works quite well.
To Carl, you're setting yourself up for a fall here. Play to your strengths. Christian girl is looking for something that you aren't and if you do manage to date her, there will be pressure to end it from her parents, church friends etc.
The thing is, most of my friends are girls. It's been that way my entire life. I've always been closer to my mom and grandmom than anyone else. It baffles me that I'm unable to simply tell a girl she looked cute without sounding like a total tool. Regardless, I think I'm going to end up breaking up with my girlfriend within a month's time, considering we talked last night for about 10 minutes and it was the most uncomfortable feeling I've had with her involved. I'm going to do the good guy thing and give it time.
As for the girl at my school, today she looked cute as heck (again) and I planned on saying something to her
She saw me in the halls, smiled, said hello, and I managed to...
Apologize profusely for being so freaking weird.
Do something super basic that can't be screwed up.
Girl: "Hi Carl"
Carl: "Hi ___ how are you?"
Girl: "Good, I'm [insert something about her life]"
Carl: Cool