Fedora... or Suse, Debian, Ubuntu, etc. — For example, with Debian/Ubuntu you'd just run (as root) apt-get install libmagickcore1 (or use synaptic, or aptitude). Note that there are other related packages like libmagick10 and libmagickwand1, which you might need to install as well.  Also, in case you're trying to build Perlmagick (as opposed to just getting to run a prebuilt version), you're going to need the respective *-dev packages, too (those contain the header files).  Finally, don't be confused by the fact that there's another whole set of similar packages for GraphicsMagick, which is a successor of ImageMagick...

Clear as mud? ;)

(From the top of my head I can't tell what the respective package names are in Fedora land, but maybe someone else can jump in...)