People love to travel, see a foreign place with different people and new realities that offer novel experiences. Ask her where she's been, how she liked it, what she did while there, and what made an impression.
If she's a townie who never ventured outside her city limits, ask her where she dreams of visiting.
It's advisable never to mention past long-term girlfriends on a first date, but past dates can be great fodder for conversation. Funny date experiences, blind dates gone wrong, and embarrassing blunders can keep things light and remind you both that you're human.
Be sure to throw in some good date stories as well, so you don't seem like a complete bumbler.
Both the bane and cornerstone of the dating world, pickup lines are an industry. Shuddering lines abound, but occasionally a girl will be surprised with a pretty decent one. Ask her what kind of lines she's received, and which ones worked. If anything, you'll learn what kind of sense of humor she has, and what not to try on her (or other women if it doesn't work out with her).
Since reality TV is replacing the sitcom as the primetime ratings machine, talk about the trend and in what dimension of reality a person eats beetle larvae for a million bucks. A word of warning: don't talk as if TV is the center of your existence. It's hard to seem interesting when your life centers around the tube.
Also, don't go into great detail about your Star Trek fixation, or the fact that you know every catchphrase ever uttered by Nicolas Cage in his movies.
If she seems like the intellectual type, discuss what's happening in the world. If you're a hermit, a quick glance at a newspaper should tell you there's some manner of commotion out there. Make sure you know what you're talking about, lest you make yourself seem dim.
Avoid getting too political or religious. If it turns out you're on polar ends of the political scale, you could end up in a nasty argument
Her friends & family
Her girlfriends are her pillars of support and cohorts in good times. Ask her about them, how she met them, where they go together, and what mischief they're always up to.
By asking her about her family you can get a good peek into who she is. What are her parents and siblings like? Where do they live? Note: if any hint of divorce or dysfunction rears its ugly head, quickly change the subject.
And since pets are pretty much family members, ask her if she has any. But you'll have to sit there and take it if she yaps on forever about her poodle.
She'll love it if you ask her about her goals, dreams and ambitions. Ask her about her ideal job, where she'd like to live, who she'd like to emulate, and how she plans on making it all happen. Find out if she has a 10-year plan.
What she does for fun
To gauge her tastes (and for a hint about where you should take her on your second date), ask her where she likes to go on weekends, what activities she prefers, and if she's a social butterfly or a lone ranger.
Ask her if she likes sports, and if so, which ones she practices or watches.
What she likes in men
This is your chance to find out what kind of guy she likes, and, if you're up to the task, subtly hint that you're what she's looking for. Does she prefer the bad boy or the nice guy? Does she like mystery or security? Does she like guys who put up a challenge?
Of course, don't ask these questions directly, but lead her that way. For instance, if she tells you about a guy she dated but promptly dumped, ask her, "Was it because he was too nice/unpredictable/etc.?"
As John Cusack proselytized in High Fidelity, on a date, "it's what you like and not what you are like that matters." That means movies, music, books, food, and all manner of consumables subject to personal preference. You can get great conversation going with this, and even stumble on things you have in common.
You'll impress her with your attention to detail if you ask her about her clothes (which she likely took an hour to pick out). Where did she get it? What's her style?