There are no easy answers to this qustion. But it certainly is very important to try to do this. Unfortunately, most children and teenagers don't get any exposure to classical music in schools, although some colleges and universities do have requirements for introductory courses on it.
And classes introducing kids to classical music must be taught very well, in a manner that will stimulate those young people. If the teacher does a boring job, it can turn students off to classical music for life. I remember how indifferent or even hostile some kids were to music appreciation class when I was growing up, and the teachers I had were actually very good.
Unfortunately, we don't have anything quite like the marvelous concerts by the late,great Leonard Bernstein for kids, although these are still available on DVD. There are SOME outreach concerts for young people,though.
It's not easy to get youngsters who love Michael Jackson, Hip Hop and Rock interested in something that is so vastly different from what they are accustomed to. Not that there's anything wrong with them being fans of these kinds of music. Our society is so vastly different from the world that produced Bach, Mozart, Beethoven and Schubert etc. What happened to me when I entered my teens was something of a fluke. I just happened to discover classical music and it changed my life forever. But I am convinced that we not only must, but can popularize classical music with young people.