I've had this done at a ton of department stores, and some of them charge for the lesson while others don't and it's just expected you buy the products they shove at you - the lesson/makeup put on you is part of the price you'll end up paying.
For a teen, I really suggest taking them into a Sephora, if you have one nearby. I've been in several locations and every time I go in with a question or need a tutorial, they're more than happy to do it for me, for free. If you go on a weekday, the odds are likely they'll be slow and bored and would love to spend all the time with you and your daughter that you need! I've spent two hours in the chair at Sephora being taught various techniques and given various samples. Some salespeople will push items on you, but they understand when you're up front and say that you're on a strict budget and your goal for the day is just getting some advice and help. I've gone into Sephoras before big occasions and the girls there have been more than happy and even excited to do a makeover for me and teach me how to replicate the look myself. Almost every time the girls have told me drugstore products I could buy that get a similar effect for a much cheaper price. Unfortunately, not all the girls working at Sephora are makeup artists. If I need the help of a trained, professional makeup artist I go into Dillard's or Nordstrom and hit up MAC. They also do a wonderful job, but the salespeople tend to be a bit more pushy about making a purchase. They offer a ton of free workshops/walk up assistance though.