The single best piece of advice I have to offer is this:
Start a writing group.
(A friend of mine who runs a homeschool learning center started some teen writing groups and I stole his idea.)
When Anne was a sophomore, and Betsy was in eighth grade, we started a weekly group. Simple premise: four teen girls, a piece of writing from each of them every week, to be read aloud to the group.
The rules for our no-pressure group were:
1. The girls could bring any kind of prose they wanted to share -- a short story, part of a novel in progress, an essay written for a school assignment, a report, a book review ... anything. It could be a first draft or something they'd polished.
2. After each reading, the first reaction from the listeners had to be a positive, encouraging comment -- what they especially liked about the piece, a favorite description, an intriguing character or plot development, etc. Then we could move on to other, more detailed constructive criticism and ask questions, share ideas, etc.
3. When we were finished with all the reading and discussion (and generally a lot of laughter and fun), the girls headed off for some free time and lunch while I re-read the papers more closely and offered editing and ideas via my trusty red pen.
4. The last rule: Don't Be Afraid of the Red Pen. Early on, I assured the girls that my red pen was their friend. (The single most important thing for young writers to understand is that rough drafts are called "rough" for a reason.) I didn't want my comments, corrections, or suggestions to discourage them. I stressed that edits do not mean, "Wow, you're a very bad writer -- oh, my, look at the many marks I had to make!" No -- I wanted them to understand that the better the writing, the more they would see my red pen (because as their writing improved they gave me more to work with.) If I taught them only one thing about writing, I wanted them to know that all the real work comes in revision. Anyone can write something; a real writer revises. And revises and revises again. I told them that I became a real writer the day I realized that a great editor was my friend.
Our writing group became the highlight of everyone's week. The girls shared silly stories, serious work, novels (completed and abandoned), essays, history reports, and stories that were composed entirely of the inside jokes of this quartet. Some weeks we (sometimes me, sometimes one of the girls) shared a writing prompt and the girls all wrote on that prompt for the next meeting. Sometimes we went out for hot chocolate and pastries. (Writers do need their sustenance.)
The greatest benefit that a writing group offers for teens is simply this: it keeps them writing. If they write regularly, they will become better writers.
And the pastries are a lovely fringe benefit.