Most Theatre Internships are generally for college students. However, if you are persistent, it is very possible you can convince them to allow you to work for them. Some internships pay, but most of them don't. If you just want to get experience working for a theater, then this is a perfect place.

I have also included a list of summer training sessions - some of them are camps; others are pre-college institutes.

Lastly, the local resources is a general list of dance studios, acting studios, and vocal coaches/teachers. A lot of acting studios and voice teachers will not accept high school students. Again, you need to get them to hear you perform a monologue or sing a song that may convince them to take you on as a student.

Good luck!