Study your teen and then recommend an activity: Each child is different and will have different interests, and that is why it is best that you study your teenage child or children to know what appeals to them. Doing this can give you many ideas for which direction to take in this regard. Once you know their area of general interest, it will become easier for you to nudge them towards that.
Make it a group project: Teenagers by nature tend to be part of groups and any project that seems okay with the group will appeal to them too. Therefore, it would be a really good idea to involve their peer group in art projects. This will ensure that they will not only participate but also see it through to the end.
Do not interfere once they start: Another thing about teenagers and art or for that matter any project to remember is that they hate adult interference. That is why, once they have taken up a project, do not interrupt them or interfere in any way. In case you feel they are going in the wrong direction, it is still better to be an observer than interfering. Soon they themselves will approach you and at that point you can help them.
Getting teenagers involved in art projects may not be easy but it does have a lot of benefits for them, which makes it worth the effort.