Installing and managing Linux software involves working with software packages in various formats. The main types are binary packages, which contain pre-compiled software, and source code packages, which contain the source code that needs to be compiled. Package management systems like RPM and APT automate the installation, updating, and removal of packages and their dependencies. Commands like yum, apt, and dpkg can be used to install packages, while tar is used to extract source code which then needs to be compiled before use.