Everyone has passions--things they do in their spare time that give them great joy. Ask about her favorite pastimes and why she loves them so much. It could be bicycling, Renaissance poetry, Paris or a favorite sports team. Maybe she knits sweaters and sells them on eBay. Maybe she collects interesting knickknacks of one form or another. The key is to find a hobby that really excites her--something she gets enthusiastic about and that allows her to talk at length more readily. Ideally, it's something you both share a passion for, which facilitates easy conversation.
Jobs can be a little more of a minefield than hobbies; not everyone is happy with her job, and you may find yourself touching on subjects--such as an evil boss or a dream career that didn't pan out--that won't bring out the best in the girl. Nevertheless, the work world can make a strong starting point for a conversation. Ask what her work entails and the various things she does to excel at it. Find out if she has any career aspirations and where she sees herself going in the future. Again, look for aspects that excite her or make her perk up in the conversation, then pursue them further.
Topical conversations are an easy way to get your foot in the door when talking to a girl, though you need to take steps to keep from appearing too vacuous. Avoid political or hot-button topics, especially early on. Instead, concentrate on movies, books, TV shows or songs she enjoys. Current releases tend to dominate such conversations, but you might try probing a bit deeper: ask about books she read as a child or older movies she might really love. Discuss music in a broad sense--her overall likes and dislikes instead of just the hot song of the moment. Quirkier bits of pop culture reveal more about her personality than the latest blockbuster and can provide insight into other topics of interest as well--science fiction if she's a "Star Trek" fan, for example, or mysteries if she mentions a love for Agatha Christie.