The National Council of Teachers of English put out an easy-to-read PDF of writing tips for parents–a list of 10 ideas to help your teen write better. Some of the highlights:
Make sure your teenager sees you writing, and encourage your teen to write more in her everyday life.
One of the most important skills young writers need is a developed writer's voice. Help your teenager develop his voice by having him write to different audiences: a letter to a newspaper editor or legislator; a story for a sibling or cousin; a recipe; etc.
Try helping your teenager "loosen up" before writing by taking 15 minutes to jot down notes or talking through ideas. These warm-up activities can be messy–the point is to get the wheels turning!
Make sure your teen has a special notebook for his personal writing.
The complete list (which I highly recommend!) can be found here: www.ncte.org/library/NCTEFiles/Resources/Positions/tips-parents.pdf