There are student saver accounts set up to encourage younger people to save. The whole point is to entice them to acquire great habits for the future.
I think it helps if the teen gets the assistance of a slightly older, trustworthy person, either a parent, uncle, aunt or family member. They could seek out the best savings plan available and then work together to save at least half of the income made through summer work or whatever. A team approach helps with accountability and discipline to save instead of shooting the whole wad. I know when my kids get money we have an agreement that at least half goes in the bank, unless if they are saving for something specific like a bike or school trip, then more needs to be put away. They have gotten pretty good about having fun with the smaller amount, in fact I think they are more satisfied knowing they have something stashed away for later.