First allow me to recalibrate everyone's expectations of what an educated fifteen year old can do or understand.
We're having one at my workplace for two weeks, who has no experience of programming. He knows how to operate a computer but is nothing like a “power user”.
We showed him how to query a database, and he's been answering questions and digging up factoids by writing his own SQL. We gave him a spreadsheet and had him compute some statistical indicators; math which was taught at school, but without the automation of a spreadsheet. And we gave him a bit of market research on potential suppliers, google-fueled stuff that must have felt pretty close to some of his school projects. At the moment he is working through a hands-on xhtml+css tutorial, which should allow him to edit some of our website next week. We did not try to impress him with our rocket science knowledge or magical powers, and he has been making himself useful to us doing things suspiciously close to programming.
Now with 30 minutes, you could start by asking her what she's seen that day, what she thinks you're involved with, explaining your role in the company, giving her a quick (prepared in advance) demo of something you work on (or anything with a quick edit-run feedback loop, jsdo.it was a good suggestion). Discuss things computers are involved with and find some she's interested in, or get her to contribute ways smarter programs could improve some activities. Half an hour is too short for practice but should be enough for a good discussion.