Start out with a fairly low heel, maybe 1.5 inches, in a shoe you can wear to school with pants or skirts. I'd suggest something with a strap or lacing rather than pumps, so it'll stay firmly on your foot.
You can just ask outright. "Mom, Dad, I was thinking I might be ready for some high heels that aren't just for prom or special occasions. Something with a heel that's not too high, so I can walk, and not too dressy, so it would be okay for school. What do you think of these?"
Then show them:
http://www.zappos.com/capezio-jr-footlight-black
http://www.zappos.com/cobb-hill-angelina-black
http://www.zappos.com/softwalk-irish-dark-red-veg-kid-leather
http://www.zappos.com/soft-style-georgette-dark-brown-speckled-tweed-vitello
(I sorted by heel height at Zappos.com. There's tons more, some of them really cute.) The biggie in convincing them might be that many of these don't have a skinny heel but something thicker or stacked, for more stability and comfort.