I've been using FC 6, x86_64, on an AMD Athlon X2, for a couple of days now. I'm trying to get oriented.
A newly compiled application library is generally put in /usr/local/lib/, but the library will be 64-bit (by default -- I don't know how to compile a 32-bit library), so perhaps it should go in /usr/local/lib64/. And the loader needs to be able to find it. I don't know what is best, but what I've done is make /usr/local/lib64 a soft link to /usr/local/lib and added to /etc/profile the line "export LD_LIBRARY_PATH=/usr/local/lib64". Is that what others do?
It's also a problem what to do about new .pc files for pkg-config. There are already pkgconfig directories in /usr/lib/ and /usr/lib64/. Mine now go in /usr/local/lib64/pkgconfig/ by default, and I added to /etc/profile "export PKG_CONFIG_PATH=/usr/local/lib64/pkgconfig" so pkg-config could find them.