In RPM-based systems (Fedora, Red Hat, etc.), you generally use the yum command:
$ sudo yum install package_name
(where package_name is the name of whatever package you want to install, not the file name, just the name)
In Debian-based systems (Ubuntu, Debian, etc.), you generally use the apt-get command:
$ sudo apt-get install package_name
If you happened to have downloaded the package file manually, then you can install them directly.
In RPM systems:
$ sudo rpm --install package_file_name.rpm
In Debian systems:
$ sudo dpkg -i package_file_name.deb
On most Linux distributions, however, if you simply double-click on the rpm or deb file from the folder navigator (Dolphin, Nautilus, etc.., the "Windows Explorer" thing), it should auto-launch an installer window.
As Mike2K said (but not in so many words), how you install software depends upon the Linux distribution you are using - YUM/RPM for Red Hat derived systems, apt-get/aptitude/synaptics for debian/ubuntu ones, emerge for Gentoo, etc. Every distribution has its favorite! IE, one size fits none... Then, there is installation via source code - an entirely different thread I think! :-)