Caroline,

Well, you've made a start -- established that you like what you saw.  But I
hate to say it, the best way to get your foot in the door is by volunteering
(don't groan, we all did it).  Not only does this help you establish
contacts, but it also gives you an idea of the variety of musuem jobs, and
this will help you find your niche.  (I started out wanting to be a curator
and wound up becoming a conservator, for example).

But be warned that not everyone is open to "free help."  An intern, even if a
volunteer, is a good deal of work because you have to take the time to teach
them (after all, you are giving your time to get something out of it).  But
don't despair, someone will eventually take you on board -- it just may take
a few tries.

Good luck!