The Online Family answers:

Teens, like all online shoppers, need to be mindful of their privacy and making purchases from only trusted merchants. For starters, you may want to check out any web sites for the stores that your teen shops at offline. Also, you should walk them through the process and note any personal information they should avoid giving out online. They’ll likely need a credit card to make purchases, so you may need to be involved in online purchases unless they have their own debit or credit card (and it’s better to use a credit card when it comes to fraud protection).