How can I "register" my library libfoo.so to link it with `-lfoo`?

How can I "register" my library foo.c, compiled to libfoo.so, to link it with -lfoo? Is it by appending its path to LD_LIBRARY_PATH? Is it by running sudo ldconfig?

For curiosity, who do I "register" it with? That is, which application "needs to know" what -lfoo means in order for gcc bar.c -lfoo to work? Is it the bash environment? Is it gcc? Is it the kernel?

Is any of this different for static libraries (eg. libfoo.a)?