You have to "Build A Relationship of Trust" with a woman. It's not as hard as you're making it out to be...you are the biggest stumbling block there is to this kind of thing, really. I think it's safe to say that you might be to concerned about yourself...you're nervous about how she'll perceive you. Being nervous is ok, they even find it a little cute, but paralyzing fear won't do you any good. Just ask questions and find out who she is. Watch how the late night talk show hosts do it. They ask a question...then based upon the person's answer, they'll select something from it and probe futher. For instance:
You: So what were some things you like to do for fun?
Her: I like to watch movies, hang out with my friends, shopping.
You: Oh yeah? What kind of movies do you like?
Her: I like a lot of movies...The Notebook.
You: Ok...did you ever see Spiderman 2? That's my favorite.
Her: Yeah, it was great!
You: Ask her what she liked about Spiderman 2 or The Notebook...just keep asking questions.
If a girl is nice or brave enough (girls can be shy too), she'll ask you questions as well. Just be cheerful, and be real. I suggest talking to girls at the cash register, or in line for something, whatever. Just make small talk and practice. It's not that hard.
Btw, you're not asking the girl to marry you. You're not interviewing for a job. You're not being held at gunpoint. Don't sweat it. If you can build a relationship of trust, present yourself well...then you can invite her to do things with you, and if there are any bumps along the way, try to resolve those concerns or move on. Don't sweat it bud.