This article is from the Audio Professional FAQ, by with numerous contributions by Gabe M. Wiener others.
There are as many getting-started stories as there are audio
engineers. The routes into the industry are highly dependent on what
aspect of the industry one wishes to enter. For instance, many
engineers who work in the classical-music field have at one time or
another been classical performers. Others enter through their work in
other musical genres, or through engineering programs at universities
or technical schools. Without exception, everyone in the industry has
learned at least a portion of their craft from watching those with
more hands-on experience. Whether this comes from a formal internship
or just from sustained observation and long-term question-asking, it
is almost always universally true. [Gabe]
 
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