As the name of this thread suggests, I've been out of the whole dating-thing for too long. I have had a girlfriend before, but that was years ago. Then I essencially got really depressed, but I've managed to straighten myself out, and got my life back on track.
Bah, she was online, but I was busy working. D:
Keep up conversation with her, and eventually ask "Hey, if you're not doing anything this weekend, wanna hang out"? Take the whole boyfriend/liking slowly with her, and you can also slip in comments along the way, should that topic come up about "Yeah, my mother was saying the same thing about me finding a girlfriend"
Yea, as >>3 says, go on a date with her, and if she's starting to talk to you more (showing interest) ask her if she could imagine to hang out with you more often.
If the time comes ask her out!
Don't be meek about the asking her out thing, just be casual. "Hey, let's go to __ on __(day or time). They have a really nice/interesting __ blahblah."
Two sentences = all you should need to say.