Start talking to your child early about the value of saving money. Since your child is living in an increasingly materialistic world, this might be a difficult concept for her to grasp immediately.
With an actual job, a teenager is more likely to see the efforts required to earn money and is therefore more likely to save it. If you only give money to your child without her having to work for it, it will be more difficult for her to understand the value of saving money.
Talk to your teenager about saving money when she gets her first job. Make it clear that, while it is tempting to spend, it is more important to save and have a set goal. Help your teenager come up with a long-term saving goal, like saving for a car, or school, or living on her own. Teach your teenager to continue saving money even after her saving goal has been reached.
Teach your child to put some of the money she has earned into a savings account. She can put the rest into the checking account for immediate access.
Set up a bank account for your teen that allows you to have access to it as well. That way, you can monitor how your child is spending and saving her money.