I've modified the original Makefile.osx from FreeImage 3.15.4 in order to compile on OS X Mountain Lion with Clang and libc++.
You will also need to add #include <string.h> in Source/OpenEXR/IlmImf/ImfAutoArray.h.
With the above modifications compiling FreeImage on ML with Xcode Command Line Tools installed is as simple as:
make
sudo make install
The above will install FreeImage in /usr/local.
Compiling and linking with FreeImage can be achieved with:
clang++ -stdlib=libc++ your_program_name.cpp -lfreeimage
These modifications are provided under the same terms as FreeImage 3.15.4.