The proper way to install it is to extract everything and copy all of the files into their respective directories in /usr/ So everything in bin goes to /usr/bin; include to /usr/include; lib to /usr/lib; share to /usr/share

You don't really need everything in the bin folder, some of those are the unit test binaries. But just copy everything anyways. The include and lib folders are only needed if you want to write or use a program that is dynamically linked against the libconsensus library provided by Bitcoin Core. I don't think anyone uses that though. The share folder contains the manpages.