sudo make install should put them where they should go, generally. It's better to install the -dev version through your package manager if you can, or just run Gentoo and use the normal package. All of those files will need to be placed in the proper include directory, which is usually something like /usr/include/<package>. The libs will also need to go wherever your distro puts them.
~You need to change your source code includes to be like #include <SFML/System.h>, with the angle brackets not the double quotes. ~ Edit: you already did that.
Double quotes are for 'local' files relative to the source file and angle brackets are for things in the system include path.