You don't. A package manager is central to a specific distribution. Gentoo, Arch, Redhat -- they all use different packaging systems. Gentoo's portage packages usually compile from source, Arch uses its own binary package format, Redhat uses RPM as packaging system -- and Debian as well as Ubuntu and Linux Mint use Debian Packages (.deb). Managing your local installation takes place using graphical frontends like Synaptic and Adept, or command-line tools like apt-get, aptitude and dpkg.

Though it is possible to install other package managers on Ubuntu (else they wouldn't be in the repositories), this is not to be recommended for the unexperienced user. One should be quite familiar with packages and package managers, how they work, etc. before even thinking about using them alongside. Otherwise it is very likely to end up with a very broken system -- as one package manager is not aware of the others, they would e.g. overwrite each others files/configurations, uninstalling a package with one package manager could break dependencies with the other, and more.

So for now I'd strongly suggest you stay with the package managers native to your system (see above).