Ahh, this brings back good memories.
I would suggest making it into some sort of incentive-style game. Once they reach $_____ in their savings account, they'll get a $__ reward. If they go under $___ they'll be deducted $___. Set a prize for a target savings figure such as a trip to where ever they want (within reason).
If you want them to learn how to invest in the stock market, tell them to play with yahoo finance and build a stock portfolio watch. Let them play with a pretend $1,000 initial investment and tell your kids that whatever they earn in imaginary $$ over the initial sum will be theirs to keep (as in you'll pay them).
After all, teens look out for #1. So you've got to convince them it's in their best immediate interest to obey you.