Are there internships or non-competitive jobs that will help an actor make connections, build up a resume, and find opportunities?

Where do you live? Where do you want to go to school? AIM HIGH! Your 'network' will begin to form in High School and College. And the stronger and broader your 'Network' is, the better your odds. For example: You get accepted to Northwestern University, in Evanston Il. That is a strong network- filled with a broad alumni list who are working professionals. (perhaps one needs an intern??!!) You are in Chicago, one of the best 'Theater Cities in America. (SO you work as a theater usher!) That allows for MORE networking. Chicago has 100 Equity Theater companies... and 200 Non-Equity Theater companies. So there are many possibilities for 'work' there. You can also start your OWN theater company ... within your Network, with your fellow students. A University like Northwesten, or Columbia, Or the University of Chicago... has "Work-Study scholarships. You can take Summer Classes at The Goodman, or Chiavgo Shakespeare... or Steppenwolf.. or Second City... in Chicago. NOW, you work as you attend school. You work WHILE you go for tori Masters. Many of your fellow aspiring thespians will do the same... and can help supply you with information, as can the University PS: Don't just study Musical Theater !! That's TOO NARROW a focus to having a LONG career. Acting, an instrument, writing, Literature, a second language.... a broad base of knowledge will not only serve you as an artist. Now, apply this same formula to Yale, Carnagie Mellon, Julliard, NYU, UCLA, Harvard, U of Illinois, Penn, etc. AIM HIGH!! ... Get on the Internet, and take a hard look at those in the field who are succeeding on the level that you aspire to achieve. WHERE did they go to school? WHAT was their 'survival job??"
Start there.
Cheers.
AC

The one thing about theatre -- everything is competitive. But often both Community Theatres and Small Professional Theatre Companies take interns -- especially if they have a summer season. While I Stage Managed at the Gloucester Stage Company in Gloucester, MA we always had high school students working as production assistants during the summer. Some of the work -- mopping floors, laundry, picking up after patrons, etc. -- may not seem like something all that inspiring, but the fact remains, the show will not go up until those things happen. My team may have had some boring assignments, but they also had some amazing ones, and they got to see the process from casting to performance.

Yes, Jill, look to audition in a local theater for confidence and development of your acting skills. The film industry does have interns, so you might keep your eyes on Variety, or Twitter and Facebook for opportunities. Studio 32 is pretty good. Of course, be friendly so you can chat with other people who might offer their insights as to where's any current auditions. Best wishes.