Understanding music is a key skill to have since you will be
working with a composer, often an arranger, musicians, and others.
Knowing how to play an instrument is not enough. You must
understand music's role in a motion picture or television
production. Music can enhance the mood of a scene or, if
inappropriate, it can kill the mood. There are college classes that
teach these principles. There are also many books on the
subject.
It also helps to have experience in some aspect of
post-production or recording. There are many technical aspects to a
soundtrack including digital recording, SMPTE time code, digital
audio workstations and programs such as Pro Tools, etc. Having
experience in the use of these tools is mandatory.
There's another element, too. Being able to work with diverse
personalities -- sometimes those involving egos and creativity --
is very important. You don't want to unwittingly insult the
director by making a comment about how the scene was edited.