A specific answer to this question depends very much on the styles and genres of music you compose/produce. However, the most common outlet for instrumental music is for soundtracks.
These days film, TV and games are all viable options. The best way to start is to get involved is with student and independent film and game producers.
For film most big unis have film schools that need lots of music for their productions. Got to screening events and on forums and get to know people and post examples of your work.
For games, most regions have meets ups and hack days that you can find out about on FB forums. Also check out blogs like http://www.thesoundarchitect.