Make them drive stick shifts. Seriously, it is that easy. You get your learners permit at 15, your manual transmission license at 16, and your automatic transmission license at 18 (if you haven't had any accidents or tickets). There'd be three benefits:
1. You physically can't text, drink, talk or even play your radio loudly when you're driving a stick shift. It is a full-body endeavor. You're listening to the engine, watching the road, and engaging all four of your limbs at the same time.
2. Passing legislation like this would create a new market for cheap, fuel-efficient cars that auto manufacturers would lease for two years, replace the clutch, and re-lease to a new driver.
3. Learning how an engine works would make teens better drivers. If they do eventually transition to an automatic, they'll be more aware of what's happening in their engine and drive accordingly.
Driving an automatic is too easy. You practically have to talk, text, zone out, or sing along with the radio to keep yourself from getting bored. Forcing teens to learn to really drive would change everything.