Take it a step at a time, our interests in gaming didn't appear overnight. Start with board/card games like Settlers of Catan or Munchkin. Play those with mutual friends, it may help build up her interest. Settlers of Catan is only a step away from Civilization games. If she has any friends that play Magic the Gathering, that can be a good start too, and the artwork may draw her in, or the collecting. Use these to bring out her interest, then try straightforward, shorter, but good games, like Portal. But don't just recommend your favorite games, ask what she's interested in. If she isn't sure, slowly try out a genre at a time. Avoid first person shooters at all cost unless you are positive she's interested in them.