Search
Ubuntu, Debian, Mint (apt)
apt-cache search [software_name]
Fedora, Red Hat, CentOS (yum)
yum search [software_name]
Mandriva, Mageia (urpmi)
urpmi -y [software_name]
openSUSE (ZYpp)
zypper search [software_name]
Arch (pacman)
pacman -Ss [software_name]
Gentoo (portage)
emerge -s [software_name]
Install
Ubuntu, Debian, Mint (apt)
sudo apt-get install [software_name]
Fedora, Red Hat, CentOS (yum)
sudo yum install [software_name]
Mandriva, Mageia (urpmi)
urpmi [software_name]
openSUSE (ZYpp)
zypper install [software_name]
Arch (pacman)
pacman -S [software_name]
Gentoo (portage)
emerge [software_name]
Update
Ubuntu, Debian, Mint (apt)
sudo apt-get upgrade
Fedora, Red Hat, CentOS (yum)
sudo yum update
Mandriva, Mageia (urpmi)
urpmi—auto-select
openSUSE (ZYpp)
zypper update
Arch (pacman)
pacman -Syu
Gentoo (portage)
emerge -uD [software_name]
Uninstall
Ubuntu, Debian, Mint (apt)
sudo apt-get remove [software_name]
Fedora, Red Hat, CentOS (yum)
sudo yum remove [software_name]
Mandriva, Mageia (urpmi)
urpme [software_name]
openSUSE (ZYpp)
zypper remove [software_name]
Arch (pacman)
pacman -R [software_name]
Gentoo (portage)
emerge -C [software_name]
For Slackware, there is no package manager settling dependencies for you, and you can use pkgtool or slackpkg. Although, there is also slapt-get which somehow helps getting dependencies.
If you have a distribution that is based an older one, even if not listed here, it will most probably have the need the same commands to install software (e.g. Ubuntu is a Debian-based distribution, so they share the same installation commands).