An important aspect of wanting to become an intern starts with discovering what it is you would like to do.
This for some people means doing some career planning either in the junior and senior years of high school or within the realm of college. Usually, this is tied in with what someone's major is. For instance, if you are a music major at a local university, you may want to explore the other avenues within music that isn't necessarily music education or musical performance. Speaking with an advisor or career counselor (if available) may be helpful to gain a deeper and more focused idea of what you would like to pursue.
Once you know what you would like - in this case, a career within music production - start looking into the possibilities of classes that you can take, as well as any type of internships in music production. There are several listings online for a variety of companies that offer summer or yearly internships. One such company is Dream Careers, which offers several listings for their music internships.
The music department may also offer information about internships or jobs that may be offering to enlist interns. Speak to the advisors, your teachers, and even some of the upperclassman in regards to this, as they may know exactly where to go and who exactly you need to speak to in order to get more information.
Consider an internship as you would any job you would want to go for. That means you will need to conduct an internship resume, along with being able to 'sell' yourself to a prospective employer that you would make a good intern for their music production company/department. As with any job interview, go into it with a cool head, a dash of confidence, and a sharp appearance.