Adrienne,
My experience with internships has been  that all
museums do not offer them.  Depending on the staff
available to supervise an intern, there may be
interns in each department of a museum, or one for
the whole institution.  Remember, an intern who is
unpaid is only a step away from being a
volunteer.  Assuming that the intern has more
technical expertise than a volunteer.  Also,
interns, even if paid are still untried and can
not be expected to replace a professional worker.
All this having been said, I found that even a
museum that does not have a formal internship
program (one that pays or gives course credit for
the work) will accept an intern  if they have put
together a proposal clearly defining the project
to be completed, the time to complete, and will
complete a written report or documentation of the
project.  The Ellis Island Museum in NYC has such
an arrangement.
does this help?
jhchin