".tar.bz2" files are archives (compressed container with files and folders inside). They can contain just about anything.
In the case of code source files, they usually come with instructions. You need to look inside the archive for those, usually named README or INSTALL. The standard drill is usually "./configure", "make" and "make install", but be aware that recovering from a failed install can be difficult. That is why distros create packages which can be cleanly un-installed.